or “unethically” (depending on your ethics!), you could just _say_ you have a competing offer. Unless there is like some secret hiring manager slack where people ask each other “did you really send that person an offer?”.
You don’t even have to disclose the company during negotiation, I’ve simply said “I have an offer from a Series A company with X equity and Y salary” so they have something to benchmark against
Sure, you can do that. But aside from the ethics of it, there's always a chance that they won't counteroffer and just say "Maybe you should go with that higher offer."
You really don't want to bring up a "competing offer" unless you're prepared to take the counteroffer/just walk away.
You did used to be able to similarly overstate your current salary, and then something quite a lot more formal than "secret slack channel" evolved. And it's often not accurate. Urgh.
How far are they going to go to validate it’s legit if you make one up?
But say you don’t want to forge one for just any company because that might not be legal. You could make your own company with a site and make offer letters that way.
All you say in this case is that "the actual offer letters are proprietary information of the company that I'm applying to and I'm not at liberty to share them" or some similar verbiage.
FWIW I've done this several times (multiple offer scenarios where I have companies compete against each other for me) and never once has a company asked to see actual proof of the other offers on condition of hiring me. If that was a condition, I would say, sorry, I'll go with one of the other ones