Will time make him see sense?

I’ve been dating this guy since mid of November everything was going perfect however up until yesterday he showed me a screenshot of this fake hinge profile of myself I’ve tried so hard to convince him it’s not me, what makes it worse is that there’s gym quotes on there and clearly I go gym he asked me who else will know that you’re a gym girl but me. It’s so unfair I really like him but it’s so hard to make him trust me he simply said he doesn’t believe me I clearly don’t have an interest in anyone else. I’m hoping with time he knows I was telling the truth, he does have trust issues cause of his past but I haven’t done anything wrong which hurts so much, I don’t know if I should just give him space or time?

Will time make him see sense?
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