The usual approach is making your purchase offer conditional on the sale of your current home, or arranging short-term bridge financing through your lender so the two possession dates can be set close together without one transaction stalling the other.
Your lawyer coordinates both closings so title moves through Information Services Corporation on the same schedule, which avoids the common problem of being contractually committed to move out of one house before the other is ready to move into.
Getting an accurate number on your current home first is what makes the whole sequence workable, since every other date gets built around it. Get your hand-reviewed valuation from Joel Dyck.