Help! Over tired baby won't stay asleep! 😭

It is currently 3:20am here and my little girl will not stay asleep for more than 20 minutes 😭 she was cluster feeding from around 9:30 and just wouldn't fall asleep after (she usually does). This resulted in her staying a wake for 4.5 hours! So now she is a very over tired baby that just won't sleep. I've swaddled, nursed, rocked, dimmed lights, played white noise, stroked her face...nothing will work! She fell asleep once but that only lasted 20 minutes and I had to hold her, once I put her in her bed she wakes up again. Someone please give me some ideas to keep her asleep. Surely she won't do this all night? Will an overtired baby eventually sleep and stay asleep? Help!

EDIT: It's currently 6:50am...She finally fell asleep at 5am while I nursed her and I sat with her for 30 minutes until I knew she was in a deep sleep and then placed her down. Well she slept but still woke for a feed at 6:30 even though I fed her ALL NIGHT! I have never been so tired in my life 😭 my first child was an excellent sleeper but I guess it all just depends on the child. I just hope she will fall back to sleep soon 🙏