Hank here from Shopify.
A number of scenarios can lead to that issue, but with your specific case, it seems to be a localized issue (such as browser or device being used, etc) as I am able to access the hamburger menu on mobile.
Rollback to an earlier version of your theme can also alleviate any issue depending on if the theme code was changed once you used the speed optimization service. It reverts back to an earlier version of your theme that worked without issues. If you do choose to rollback your theme, ensure you make a duplicate copy of your theme prior to this step.
Additionally, it can come down to the theme you are using, as support differs based on the theme, but I am confident the above will resolve the issue for you.
Let me know how you get on, or if you have any additional questions.
All the best,