There's little else you can do besides making your characters "people". I.e. create and depict them in ways that, in the reader's perspective, lift them out of the "paperdolls" box, towards if not into the "actual people I know" box. There are dozens of ways people can feel empathy towards other people, and it's important to remember it. Trying to make every primary character into a reader's almost-real friend or crush or idol is not gonna work unless your audience is 5.
The minimum is one character the reader cares about. If that connection is strong enough, the reader will also feel about the characters that one character cares about, and characters that affect their situation.
Immersion is another thing. One doesn't want a reader to be too aware they're reading a written work. The best stories are like stepping through a door into another life, and the worst are, well, like reading a bad story. Superficial quality is a major aspect, thankfully it's easy to keep in check. Actual flow and grip is much harder to learn and sadly I don't know any other ways to make even a basic check on them other than letting the story sit for a few weeks after finishing it, and reading it again, aloud. Getting a good beta reader or another source of frank feedback is essential here.