How to begin preparation for the MAT?

Just dive in, really. Start with some of the older past papers, do questions. Refuse to look at the solutions for days. Try different approaches even if you get the question right, see if there's a faster way, etc...

Do ya know where the older past papers can be found? On the Oxford/Imperial website there's only the more recent papers!

Thanks!

Start with the oldest one on the website. There's a MAT prep thread on TSR that'll link you to the even older papers but i cba looking it up rn. I'd still advise doing the oldest of the most recent lot. So starting from 2006/7 sounds optimal. Then goging back to the older ones once you've done up till 2011/12.