Almost certainly nothing to do to the seat tube.
If its not suspension it should be cheap to replace the seat post with a shorter one; or even to cut down the old one. If you've got a local community bike hub they may swap a short one for your longer one. That'll only help if it is the length of the seatpost that is stopping the saddle going any lower.
If it's suspension it will be more expensive to replace with another suspension. Also, most suspension seatposts still leave a significant saddle height over seat tube even at their lowest.
Depending on the saddle and saddle rail support you can sometimes hang with the saddle rails 'upside down' and save an inch or two in height. Some rails make that impossible, or for a low saddle it can mean the top of the seatpost meets the underside of the saddle, very uncomfortable.
Once you are comfortable with it you are probably best off cycling with saddle height so you can only get one foot on the ground at once. Otherwise you won't be extending your legs/knees at their most efficient while pedalling.
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https://bicycles.stackexchange.com/questions/37583/can-a-saddle-clamp-be-upside-down-on-a-childrens-bike
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