Assuming you are talking about a reserve retirement...
My 20 year letter didn't get to me until three months after I had my 20 years.. I received my 20 year letter in 2017 but didn't retire until January of 2023. The "powers that be" recommended starting the process six months out from when you intend to retire. I started a year out and they barely completed everything a month and a half before retirement. There were circumstances where my retirement packet just sat on someone's desk because it was missing something, and no one notified me. FWIW I was full time in the guard and able to urge things along. I understand the desire to avoid more months of fun, but sticking around could help avoid the out-of-sight out-of-mind aspect. YMMV, but retiring a month after making your 20 good years is probably not going to happen.
Also, my FERS retirement took six months after my 60th birthday to process, despite being turned in 13 months prior.