Excuse me from saying this, but didn't it warn you that you have to write them down? It wasn't an optional procedure, if you don't have the seed phrase you're reducing your chances to restore your wallet. I mean it kinda warned you for the consequences...

A .dat file? Where did you get that from? Ledger? Well, if I were you, I'd install Bitcoin Core and I'd try to import it.

Open up Bitcoin Core and click on Window —> Console. Back up your .dat file and type the following:

If that worked and it imported it successfully, you can get the private key by entering the following: