Solved

starting design

how do some managers start the season with a car so advanced while others start the season with really low spec cars in the same league?

Example? League?

The 2 main reasons for a worse car would be:
-Chief Designer rated lower (less stars, note that you see the rating of other teams staff relative to your level, what counts is their rating, aka how high their staff level is compared to their team level)
-The team was just promoted
-The team joined the league mid-season last season

Promoted by???

Promoted from rookie to pro, or pro to elite. A newly promoted team only gets around 260 or less design points at the start of the season iirc, while most of the other teams that have remained in their tiers and completed a full season would start with somewhere around 310-340dp depending on Chief Designers used and their star ratings.