I'd be skeptical of your ability to patch a hole on the bottom, and near the outside of an Intex. My guess is, that pool is shot.
But IF:
+ you drain & dry the pool, AND
+ use some scrounged material from another Intex pool, AND
+ the hole is in a FLAT area (not near the seam), AND
+ you apply patches on both the inside and the outside
THEN you might succeed.
But if the pool was installed on level smooth ground, it sounds like you have an OEM defect. The Intex pools are a fantastic deal -- compared to 'old-school AG pools' -- but Intex quality control leaves something to be desired. The quality and construction on most of their pools is good, but maybe 10% have some sort of OEM defect and maybe 2 - 3% have a 'show-stopper' defect, like yours may be.
If it's a defect, call Intex. They are a bit of a pain to deal with, since all the staff members I've spoken with only speak Chinese or 'Chinglish'., which makes communication difficult. But they do seem to be pretty good about warranty replacements of bad product IF you act promptly.
If it's your boo-boo, and your kids want to swim NOW, you might see if you can swing the cost of a new replacement. Save the old pool pump, fittings, and some fabric, so you are 'set' for repairs to your new pool, if needed.
Good luck!
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