I think the Bahn is overestimating the time to go from the S-Bahn to the ICE. Two years ago, we came into the ground level part of the Hauptbahnhof on an RE from the direction of Würzburg and transferred to the S-Bahn in the underground (tief) station. I don't think it took 10 minutes to do it. There are escalators from the middle of the platforms (101 - 104) in the S-Bahn station to the main level of the Hauptbahnhof. I think one escalator goes to the parking garage under the front of the station and the other one to the main track area. They should be clearly marked, to the parking garage with a sign with a letter P with a roof over it and to the trains with a picture of a train. There are also elevators from tief to the ground level track area. From the map, it looks like it is elevator number three. Here is the map; the S-Bahn station is on ebene -3 (third underground level).
When using the map, notice the direction of north (0----->N). Although the S-Bahn tracks are shown running left to right on the map, they actually run parallel to the tracks on the main level, which are shown running vertical.
Here is a picture of the ground level end of the escalators to/from the tief station. The escalator comes up opposite track (Gleis) 15. Looking at tomorrow's schedule on the Bahn website, ICE 625 will leave on track 7, 4 platforms away from the escalators in the same direction that you come up. That could change on the day you travel, but I would bet 625 will leave from a track near 7 on the day you travel. If you have internet access, check with the Bahn website a few days before you travel for the track number. It should be posted at least a week before. Actually, if might be posted on June 14, when the schedule for the 2nd half of 2020 is posted.
If you want more time, click on "adjust the transfer time" above the ICE 625 connection, then click on "arrive earlier ...". It will show you a connection leaving St Goar earlier and giving you about 40 minutes to make the connection in Frankfurt.