Start Date Advantage/Disadvantage?

I'm starting FT at a boutique consulting firm this Sept/Oct and I'm looking for some insight regarding if there are any disadvantages associated with a "late" start date. I was given a date preference between summer and fall and chose fall because I'll be relocating halfway across the country and wanted to spend time with family/friends, travel, and take the GMAT before I start work. I noticed that most start dates at other firms are in July and I'm concerned about how my timing may affect staffing prospects, upward mobility/promotion timelines, socializing, etc. For example, could I end up on the bench when I start because many projects get assigned in the summer?

Any insight would be appreciated.