I'm showing 20-200ms longer on first run of the exec. Modified the test script a bit to show that it doesn't happen again if you modify the executable's contents.
echo $'#!/bin/sh\necho Hello' > /tmp/test.sh && \
chmod a+x /tmp/test.sh && \
time /tmp/test.sh && \
time /tmp/test.sh && \
echo 'echo Hello2' >> /tmp/test.sh && \
time /tmp/test.sh
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