Most first-time candidates accept the first number out of relief that an offer exists at all. That relief is understandable and usually costly.
Base salary is rarely fixed
Recruiters typically have a band, not a single number, and the first offer is rarely the top of it.
Equity and sign-on bonuses are flexible too
If base salary genuinely cannot move due to internal banding, these are often where a company has more room.
How to actually ask
A simple, non-adversarial request — “is there flexibility here, given [specific reason]” — costs you nothing and is expected by most hiring managers.