Q: How can I migrate data from an old MBA to a new one without having access to the screen of the old one? The screen of the old MBA is damaged !

If the old MacBook Air has a Thunderbolt port, connect them with a Thunderbolt cable and start it up with the T key held down.

(110259)

Connect it to an external monitor. You can't migrate using MA unless you can see the screen.

If your "older" MBA has a Thunderbolt port then it isn't that old. See Target Disk Mode about how it's used. Note that without a monitor you won't be able to tell from the screen when it has fully started, and if it succeeded in starting in TDM. If it did, then the hard drive should appear on the Desktop of your new computer. You can then access it to transfer your files. You can even use Migration Assistant or any backup utility to transfer data. Just don't try to transfer system files.