C (gcc), ³³ 29 bytes

x;f(n){for(x=0;++x!=n;n/=x);} 

Try it online!

How

Uses the gcc C extension: ++<var1>! = <var2> as ++x!=n which increments x until x! is equal to n. ¯\(ツ)/¯

C (gcc), ^{33 29} 28 bytes

Saved a byte thanks to ceilingcat!!!

x;f(n){for(x=0;++x-n;n/=x);} 

Try it online!

C (gcc), 33 bytes

n;f(x){for(n=0;++n!=x;x/=n);x=n;} 

Try it online!

How

Uses the gcc C extension: ++<var1>! = <var2> as ++n!=x which increments n until n! is equal to x. ¯\(ツ)/¯

C (gcc), ³³ 29 bytes

x;f(n){for(x=0;++x!=n;n/=x);} 

Try it online!

How

Uses the gcc C extension: ++<var1>! = <var2> as ++x!=n which increments x until x! is equal to n. ¯\(ツ)/¯

C (gcc), 33 bytes

n;f(x){for(n=0;++n!=x;x/=n);x=n;} 

Try it online!

How

Uses the c operator ++<var1>! = <var2> as ++n!=x which increments n until n! is equal to x. ¯\(ツ)/¯

C (gcc), 33 bytes

n;f(x){for(n=0;++n!=x;x/=n);x=n;} 

Try it online!

How

Uses the gcc C extension: ++<var1>! = <var2> as ++n!=x which increments n until n! is equal to x. ¯\(ツ)/¯