Newsflash: How to buy a home while selling yours

My husband wants to move and pay cash but the problem is we can’t afford to move unless we sell our current home. We talked to a realtor that said we could list the house and put an offer on another house and just close on the same day. But this doesn’t seem realistic to me because I don’t even know if anything we like will come on the market before selling our place. Is there any options other than loans because for some reason my husband is also against that