Community addition: Since this answer was written, new functions have been added to PHP, suggested in respective answers: array_key_first() (PHP 7.3+) and, finally, array_first() (PHP 8.5+).

Original answer, but costly (O(n)):

array_shift(array_values($array));

In O(1):

array_pop(array_reverse($array));

Other use cases, etc...

If modifying (in the sense of resetting array pointers) of $array is not a problem, you might use:

reset($array);

This should be theoretically more efficient, if a array "copy" is needed:

array_shift(array_slice($array, 0, 1));

With PHP 5.4+ (but might cause an index error if empty):

array_values($array)[0];

There's no need to use all above mentioned functions like array_filter. Because array_filter filters array. And filtering is not the same as find first value. So, just do this:

foreach ($array as value) {
    if (meetsCondition($value)) {
        $result = $value;
        break;
        // or: return $value; if in function
    }
}

array_filter will filter whole array. So if your required value is first, and array has 100 or more elements, array_filter will still check all these elements. So, do you really need 100 iterations instead of 1? The answer is clear - no.

You can loop through your array and end the loop when you find a match using break:

foreach($arr as $value) {
    if(preg_match($pattern,$value)) {
        $return_string=$value;
        break;
    }
}

To specify a limit:

$limit=3;
$i=0 // sets the number of returned results to 0
$results=array();
foreach($arr as $value) {
    if(preg_match($pattern,$value)) {
        // add the result into the array and increment the counter
        array_push($results,$value);
        $i++;
    } if ($i=$limit) break;
}

You can then use another foreach loop to return your values like:

if(count($results)>0)
foreach ($results as $result) {
    echo $result;
} else echo "No results found";