When I asked him why he wasn’t honest from the beginning, he said things like “what does this change?”
Well, it means he's untrustworthy for a start.
You're asking how to rebuild trust with someone you know has lied about something as insignificant as his age.
As other have said, it's fairly normal to change slight details when first chatting to someone online to anonymise yourself (eg change your age by a year, not give your exact location, etc) but you'd expect to clarify those by the time you were actually dating them.
I wouldn't consider any of that to be a breach of trust.
So, if someone has lied to the point of you needing to rebuild trust in a LDR after a year, I wouldn't bother.
I don't know much about LDR but I'd assume that they require complete trust to work. I certainly wouldn't be thinking of relocating to be with someome I didn't trust.
Rebuilding trust only really works in long term relationships where people have an extensive, positive and supportive history to call on from which to rebuild and, even then, it's difficult and there are no guarantees. Otherwise, it really just amounts to asking, "How can I ignore the response of nervous system that is designed to protect me and push these feelings down so that I can remain in this relationship?"
You have no idea what else he has lied, or will lie, about.