You can't make new accounts on twitter. You can only use existing apple or google accounts.
I think you can, if you install their app.
I don't have a smartphone.
Then use one of the other options. It's not really that difficult.
The options are: install the app or register using a google or apple account. Since the former is the same as the latter it all collapses down to: register using a google or apple account.
I have neither a Google account, nor an Apple account.