Cubase 14 shifts my recording early!

One would need to setup the “Record Shift” value:
grafik

It is in Studio → Studio Setup → Audio System
61 samples is the value in case your project ran on 44.1kHz sample rate. If you used another sample rate you have to convert 1.38ms to samples with your sample rate.
I don’t know if the value needs to be positive or negative, you’ll find out by trying.