Zelle does NOT require the little deposits. You have access and can send funds within seconds of signing up. Note Zelle is the service but each bank brands it a different way. Chase is called Quick Pay. Every bank seems to have a different name for the service. Look for it where the payments are listed. And DON"T LOOK for Zelle, but look for some pay something, Surepay, quick pay, send money, something.
If you have a checking account at a bank that uses Zelle. You have to activate the service and provide a phone number of email address that the system uses to find YOU. The other person needs to set up theirs too. It literally takes 10 seconds. It likely takes you longer to find the link to set it up on your banks website, than it does to set it up. You don't need account numbers or routing numbers, it just has to one of the 2 dozen banks that Zelle works with. You put in someone's email and the funds and it enter. The money is there in seconds. It doesn't matter which bank you belong to. And Zelle is free of charge AFAIK.
With Bill Pay that cuts a paper check, at my bank, which is chase, it shows if checkin pending or cashed, and if cashed you can look at an image.
You need to investigate what your bank cam do nowadays. Not sure who you are banking with?