This is a just rough method with rough results...
cat ctest.bash
URL=http://localhost:8080
while true
do
curl $URL 2>/dev/null || continue
echo
echo "Success from $URL at $(gdate +%T.%N)"
break
done
$ ./ctest.bash
$ gdate +%T.%N ; docker run -p 8080:8080 some-docker-image
11:59:43.615812000
2019-05-10 09:59:44,252 INFO [io.quarkus] (main) Quarkus 0.12.0 started in 0.004s. Listening on: http://0.0.0.0:8080
2019-05-10 09:59:44,252 INFO [io.quarkus] (main) Installed features: [cdi, resteasy]
# ...and the ctest script then says
hello
Success from http://localhost:8080 at 11:59:44.950311000
$
At this point we can rouhgly compute
11:59:44.950311000 - 11:59:43.615812000
For a total startup time of about 1.3 seconds.
It's rough...looping curl in this way takes some time, but running the test several times should give a ballpark figure.