Time required to activate JRPass

Hello
In the second half of June we, a family of 4, will arrive by ferry from South Korea in Fukuoka/Hakate.
We have 90 minutes from arrival with the ferry and the last train to Hiroshima.
Is 90 minutes enough time to arrange a JRPass activation and book this train. Or will it take longer?
I understand I cannot activate the Pass outside Japan.

Thanks, regards

André