Logstash starts slowly PERIOD! 
30 seconds is actually pretty quick. Some of our more complex pipelines can take 3-5 minutes.
NOTE: This is one of the reasons why it is wise to split Logstash into "collection" instances and "processing" instances, with some sort of queuing in between such as redis or kafka. This allows you to make changes to your processing instances and restart them, without missing any incoming data due to long restart times.
You don't mention which version of Logstash you are using. If it is prior to 5.5.0 then you can speed up start times by adding the following to your jvm.options file.
# Entropy source for randomness
-Djava.security.egd=file:/dev/urandom
That was the only trick in the past, and it is standard since 5.5.0.