Recently laid off | 5yoe backend dev | Should I disclose my layoff?

Got laid off in Feb (cost cutting, not performance). Actively interviewing and getting calls.

when I say I’m an immediate joiner, recruiters ask why I left without another offer. So I’ve been saying I have an offer from an early-stage startup (not planning to join) and using that to justify ~50% hike expectations.

Now I’m worried:

•	Will companies verify this and ask for proof of offer?

•	Can this backfire at offer stage / background check?

•	Is there a better way to handle this without getting filtered out early?

Honestly just trying to stay in the process since being laid off seems to reduce chances.

Anyone been in a similar situation?