Cash removes financing risk specifically, not every condition. An inspection condition, a condominium document review or a sale-of-buyer's-property condition can still be attached to a cash offer, and any of those can extend the timeline the same way they would on a financed deal.
The lawyer's side of the file, title search through Information Services Corporation and preparing the statement of adjustments, still has to happen regardless of how the purchase is funded, so a rushed possession date needs your lawyer's confirmation as much as it needs the buyer's cash.
How fast your specific transaction can actually move depends on which conditions are attached, not just whether cash is involved. Get your hand-reviewed valuation from Joel Dyck.