This is a good question.
I’d suggest you examine the date on each check. It’s relatively common for people to post-date wedding gift checks for the actual wedding day, so you can’t actually deposit those beforehand. Otherwise I’d deposit them immediately knowing that many people don’t keep registries and if you wait months and then cash the check it might throw off their balance. If you cash them immediately, then I recommend you also immediately write your thank you note.
However, I would suggest that any check that arrives less than two weeks before the wedding be held and not deposited until after the wedding. I say this only because some people who give late gifts will assume the check won’t be deposited until after the wedding, and may not have money in their bank until that date.
I would cash it ASAP!!