I do think excising the first part would be more streamlined—-this is what Harry Potter did. Exposition shouldn't be delivered clumsily, however; maybe the protagonist mentions wishing his old parents were still alive during an argument with his new guardians. Arguments are actually efficient ways to deliver AsYouKnows because they are usually when people are reminded of things.
she/her/they | wall | sandboxA few thoughts:
You could perhaps start the narrative with the funeral, something emotionally impactful as a bit of a hook, and then dribble in bits and pieces about the protagonist's family life during the narrative.
Another thought might be that, if the structure of the story allows, you could use flashbacks to show parts of the pre-timeskip section.
And finally, let me ask: how important are the backstory elements to the main narrative? Can they be cut, or shown in brief?
My Games and Asset PacksThen I suppose that my next question is this: Does the backstory provide the same sort of central attraction that the main story does? That is, if for example the main story is action-heavy, is the backstory similarly so?
If so, then perhaps you could keep it at the start; if not, it might become a slog for readers to get through in order to reach the bits that they're interested in.
In the latter case, what you might be able to do is to sprinkle the backstory throughout the narrative, revealing bits as they become relevant. If there's sufficient detail, this might be done in the form of flashbacks, perhaps.
My Games and Asset Packs

The protagonist of my story is someone who was sent off to live with a relative after one of their parents died. As I've planned things so far, my story starts before their parent dies. After they die, my protagonist learns they'll be sent away and then there's a Time Skip of about a year or two, which picks up with my protagonist living with their relatives. Now I'm debating getting rid of the first part of the story and just starting with my protagonist living with their relatives. I think this would streamline the story a bit, but I have some issues with this approach:
1. I don't want to stop the story to explain my character's backstory, when I could just show it at the beginning. This is especially going to be an issue as a big part of their character arc has to do with their feelings about losing a parent and then being sent away.
2. I want to contrast my protagonist's old life with that of his life living with his relatives. I feel if I show what their life was like before being sent away, I won't have to constantly have my protagonist constantly tell the audience how their life was different.