To whoever it may help: I had the exactly same issue as the op.

Created a wallet with blockchain.com, didnt save the backup words and didnt save my Wallet ID.

I opened a support ticket with them, providing the date the wallet was created and my password.

2 days later they replied with my wallet ID.

I was very afraid to provide my password, but they say they can look up for an wallet ID only if you provide the estimate date it was crested and the password.

I was afraid someone from their support team could just acess my wallet and retrive my 2 Btcs, but they were 100% honest! Provided my wallet ID, and my 2 bitcoins were still there when I logged in.

Hope it can be useful!