#MATL, 12 11 bytes

1 byte saved using Dennis' idea of computing -1 raised to the input string

1_j^Ys0<f1)

Try it online!

1_         % number -1
j          % take string input
^          % element-wise power. This transforms '('  to 1 and ')' to -1
Ys         % cumulative sum
0<         % true for negative values
f          % find all such values 
1)         % pick first. Implicit display

MATL, 12 11 bytes

1 byte saved using Dennis' idea of computing -1 raised to the input string

1_j^Ys0<f1)

Try it online!

1_         % number -1
j          % take string input
^          % element-wise power. This transforms '('  to 1 and ')' to -1
Ys         % cumulative sum
0<         % true for negative values
f          % find all such values 
1)         % pick first. Implicit display

#MATL, 11 12 bytes

1 byte saved using Dennis' idea of computing -1 raised to the input string

1_j^Ys0<f1)

Try it online!

1_         % number -1
j          % take string input
^          % element-wise power. This transforms '('  to 1 and ')' to -1
Ys         % cumulative sum
0<         % true for negative values
f          % find all such values 
1)         % pick first. Implicit display

#MATL, 12 11 bytes

1 byte saved using Dennis' idea of computing -1 raised to the input string

1_j^Ys0<f1)

Try it online!

1_         % number -1
j          % take string input
^          % element-wise power. This transforms '('  to 1 and ')' to -1
Ys         % cumulative sum
0<         % true for negative values
f          % find all such values 
1)         % pick first. Implicit display

#MATL, 12 bytes

2*81-Ys1=f1)

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2*         % implicit input. Transforms each '(' into 80 and each ')' into 82
81-        % subtract 81. Gives array with -1 for '(' and 1 for ')'
Ys         % cumulative sum
1=         % true for values that equal 1
f          % find all such values 
1)         % pick first. Implicit display

#MATL, 11 12 bytes

1 byte saved using Dennis' idea of computing -1 raised to the input string

1_j^Ys0<f1)

Try it online!

1_         % number -1
j          % take string input
^          % element-wise power. This transforms '('  to 1 and ')' to -1
Ys         % cumulative sum
0<         % true for negative values
f          % find all such values 
1)         % pick first. Implicit display