The space shuttle stack has a net thrust (thrust minus weight) of about 9 MN at lauch [1]. High carbon steel has a yield strength of 700 MPa [2]. So you need a piece of steel with a cross section of 0.013 square meter to hold it down. That's a rod 6.5 cm / 2.5 inches in diameter. Hardly impossible. Your nearest road suspension bridge probably has cables bigger than this.
replyIf you want to argue that it's impossible in practice, I'll point out that SpaceX's Starship first stage has a net thrust of 53 MN [3], and it does static fires (without the weight of the second stage on top) [4].
The space shuttle didn't do static fires because of the solid rocket boosters that would need to be teared down and reconstructed afterwards; not because it's physically impossible to hold it down.
[1] https://en.wikipedia.org/wiki/Space_Shuttle
[2] https://www.unionfab.com/blog/2024/03/yield-strength-of-stee...