It is possible, but the sellers have to agree to do it. There are several ways in which to encourage the sellers to do so:
1. Set a date by which time if your house is not sold, you will agree to go forward with a bridge loan.
2. Allow the seller to continue marketing their house; if they get a like offer or better, ask them to give you # days to perform or you will let the contract go to the next buyer. At that time, you can active a bridge loan and move forward or give the house up. The seller will not have lost any opportunities.
3. See if you can qualify for a mortgage without the sale of your home.
4. If the seller does not have any time restraints, your offer and terms are good and you are providing a lender pre-commitment with the only contingencies being contract and appraisal, they may agree to wait.