All 1955, 1956, and 1957 Thunderbirds were built to mount a hard to or a soft top. If you look behind the seat you will find 2 studs on each side for mounting the swing arm that allows behind the seat storage for the soft top. Only very early 1955 cars may have a single hole deck plate for securing the rear of the top. all others will have a two hole plate that allows either top to be mounted. Additionally the windshield header has the cup shaped mounts for securing the front of either top as does the mounting plate on either side of the drop curtain area for securing either top to the sides. Although a swing arm assembly is not necessary for use of a soft top you will find it is invaluable for using the top. When you purchase a top make sure you get the swing arm assembly with it. After market soft tops are available through any of the Thunderbird specialty suppliers. Additionally Jewell makes a reproduction that meets factory specifications.
good luck to you. when we bought our '57 a bit over 25 years ago we had only a
hard top. We purchased an after market soft top with swing arm and have used it ever since. Our top while purchased from Councours
Parts was drop shipped from Prestige Thunderbird
parts as the manufacturer. This is the only aftermarket soft top I have personal knowledge of and can recommend.