Hi!
Usually I'd say start timed questions when you're confident in your ability to answer the majority of questions in the question pool (excluding curveballs). When starting, I'd also say don't worry about the time limit as much because it's something you still have plenty of time to work towards - focus on getting the questions right instead at first. Afterwards, in the lead up to the exam focus on finding the balance between speed/accuracy that maximises your result - you don't want to rush and screw up, nor you do want to leave too much blank. Slowly build-up question recognition, confidence and speed and find your level, I suppose. Don't worry too much either if people are starting to do mocks and stuff before you, everyone does things at their own pace. While I wouldn't be surprised if people rushing into mocks did well, I also wouldn't be surprised at all if you outperformed some of them either.
I get that UCAT is a bit daunting - it definitely was for me too! Getting questions wrong and losing confidence starts a really crappy cycle of losing confidence -> not practicing -> getting questions wrong -> losing confidence etc. I got stuck at the second step for the longest time - easiest way to break it is do some untimed easy stuff where you focus on getting stuff right. It's a long grind and still quite a long way away so don't feel too stressed out about it.