I haven’t signed agreement yet
Less relevant than you might think - you've already entered into a contract of employment with them.
If I leave this workplace, will they give me P45?
Yep. You've been employed there, even if only for a few days plus whatever notice period they make you serve (if any) and they have to pay you for that. Paying you means all the wonderful HMRC gubbins that come along with that and thus a P45.
What make a start of employment with a company?
The commencement date as outlined in your offer/contract - in the absence of that or of any paperwork to the contrary it will be the first day you worked.