Generate string subject to first two bytes of SHA256 of this string equal 0

I have a string s like:

username-password-{random}

I would like to generate the hash SHA256 of the string s, such that first 2 bytes of the hash equal to 0, like:

0000afcbd546843....

So, username-password- is fixed and we can random the {random} part, is there any way to control the random part to get the SHA256 satisfy that condition.

I have the code bash script below, but I have run many time, it does not meet the condition.

pt="0000"
counter=10000000
while [ $counter -le 20000000 ]
do
        echo $counter
        fibyte=$(echo -n ""username-password-"$counter" | sha256sum | cut -c1-4)
        if [ "$fibyte" == "$pt" ]
        then
                echo ""username-password-"$counter"
                echo =======================================================
                break
        fi
        ((counter++))

done
echo DONE