I always get my MOT done early and as close as possible to a month before it’s due, so if it does fail, then it can be repaired and re-tested in good time - before the MOT due date. As Guzzle has said, with the first MOT, it’s worth getting it done early so in the unlikely event it fails on something that’s covered under warranty, it can be fixed free of charge.
If @Sootchucker’s MOT is due on 03/05/2021 and he got it carried out, say two weeks before the due date (19/04/2021), this doesn’t adversely affect the expiry date on the MOT cert; the MOT station should show the dates on the cert as 19/04/2021 to 03/05/2022.