Also, after Paxton and Scott bonded, we get to see the whole family eating together and talking about Cassie's day, with Paxton pulling out a video he made with his phone to show it to Scott. It's just a small gesture, but it's how naturally it comes out that shows that they really bonded.
Scott's first scene shows him in what seems to be a ruthless prison fight with Peachy, a fellow inmate. After punching Peaches across the face, instead of getting his ass kicked in return it's revealed that it's a ritual for anyone getting out of prison, and Peaches plus all the other inmates are soon to embrace Scott to show they're happy his sentence is up.
Peachy: Im gonna miss you, Scott! Scott: Gonna miss you too, Peachy. (They exchange a hug and a handshake) Man, you guys got the weirdest goodbye rituals.
Although the toy rabbit that Scott gives Cassie for her birthday has a rather Uncanny Valley appearance, she cherishes it despite outright stating that it's ugly, and is shown with it numerous times throughout the film.
Cassie: He's so UGLYYY! I LOVE HIM!
For extra heartwarming points, the fact that Cassie loves it so much and that her mom offers a replacement toy (that is rejected) shows that Scott knows his daughter better than Maggie does, even though he's been in jail for a good chunk of her life.
One alternate reason for Cassie loving the ugly rabbit, is because her father gave it to her, as well as most likely having very little things from her father.
Hearing his daughter's voice calling out for him is what gives Scott the willpower to escape being trapped in subatomic space.
During the climactic battle when one of Scott's discs accidentally causes an ant to grow to the size of a person, right in front of Cassie. What does a small child do, when suddenly faced with an enormous, chittering mass of armor plating and pincers? Gape in awe, with a look that says she's already decided that it's her new pet!
The fact Scott cared so much about Antony, his flying ant mount. Enough to swear revenge on Cross for blowing him to bits during the final battle.
One of the things Scott uses the Ant-Man powers for? Visiting his sleeping daughter before his heist on they Pym facility.
After the battle with Yellowjacket, Scott is seen eating dinner with his daughter, ex-wife, and Paxton, now the hero his daughter always thought he was. Paxton even shares a video with Scott of Cassie doing her first cartwheel, which the man with superpowers finds more amazing than what he has done. It's possible Scott may even be living with them now, as evidenced by the enlarged ant Cassie treats like a dog.
A trailer includes a version of Hank's prison speech that's a good deal more encouraging to Scott.
Dr. Pym: Scott, I've been watching you for a while, now. You're different. Now, don't let anyone tell you that you have nothing to offer.
"He said yes." Welcome to the Avengers, Mr. Lang. What's even better is that Sam, whom Scott accidentally fought, vouches for Lang as a new member or at least an ally for the New Avengers.
Scott develops a genuine bond with the ants that he controls, treating them like loyal friends instead of the numbered masses that Hank does.
His cooing over how cute one of the crazy ants is before it jumps into his arms like an excited dog greeting its owner.
It turns into a mix of this and Funny Moment when the other crazy ants decide they all want to greet Scott too.
The way Scott talks to him like he's a puppy really sells it.
Scott: 'Das a good boy!
While gearing up his ants for the Stark compound heist Scott gives each ant in line a little pat on the rump as they file through. And considering that's where their heart is located...
Luis apologizing to Scott when they find out that the vault they're breaking into only contains the Ant-Man suit and nothing of real value where they're concerned, knowing Scott was counting on getting money so he could see Cassie.
Hope and Hank reconcile after Hank tells her the truth about what happened to Janet. They share a very emotional moment, until it's ruined by Scott.
The scene that leads up to it with Hope and Scott in the car.
The fact that Scott is okay with being expendable on this mission, even with what it would put his daughter through. Whether because he's completely aware of the stakes or just understands how much Hank wants to keep Hope safe, Scott knows full well he might die or spend the rest of his life in prison, and doesn't flinch.
Luis, Dave and Kurt going out of their way to help Scott during the climax. They are ex-convicts risking massive prison sentences, and as far as we know, they aren't getting paid. But they still do whatever they can, including stealing a cop car and going to Paxton's house to try and help Scott, all because they want to be "the good guys" for once. Of course, even good guys have limits.
Luis takes time to drag a guard he'd previously decked out of the building before it implodes.
When Scott gets fired from Baskin-Robbins, Dale, his now-former boss, comforts him by telling him he was a big fan of his previous heist and is a lot more accepting of Scott than most others, but sadly, he still has no choice but to fire him. Dale, further showing he's not a Bad Boss, allows Scott to take a free smoothie, assuring him it'll totally be off the books and he'll look the other way. While it's not much, it's the thought that counts. Scott takes him up on the offer too.
Small one, and a little odd given the circumstances, but when Cross shoots Hank, Hope yells "Dad!" which is probably the first time in years she's called him that.
When Scott's in the Quantum Realm, he sees flashes◊ of what seems to be Janet Van Dyne. Her presence shows that Hank has a chance at saving his wife, and, seeing how she appears multiple times, could have helped save Scott, as she could have thought that her husband was finally coming back to save her, but as he was badly injured, she helped him return instead.
Maggie reassuring Cassie.
Cassie: Mommy, is Daddy a bad man? I heard some grown-ups talking. They said he was bad.
Maggie: No, he's not bad. Daddy just gets confused sometimes, you know?
Hank's actual speech in the film to reassure Scott that he is the man for the job.
Hank: It's too late for me, but not for you. This is your chance, your chance to earn that look in your daughter's eyes, to become the hero that she already thinks you are. It's not about saving our world. It's about saving theirs.
Scott's Apologetic Attacker tendencies and obvious admiration towards Falcon shows that even with the incident in Sokovia, people still look up to and respect the Avengers.
Considering all the time they took to made sure that civilians were safe, and that they risked and lost their lives to do so, it might as well be because of what happened in Sokovia.
At the end, after Hank talks to Scott about coming back from the Quantum Realm, he takes a moment to muse: "Is it possible...?" for Janet to come back as well. Hank is an old scientist, one of the world's best, and his mind is no less sharp despite his age. He might make the journey into the science of the Quantum Realm once more, and with hard work and experimentation, see his first love again.