When viewing the main 'Shopify Community' page, there are several boards you can choose from. The first couple are 'Announcements' and 'Discussions'. You can't start a topic in those, but you can choose from other boards below them on the list.
For example, if you click on 'Feedback on my store', you'll be taken to that specific board where you can 'Start A Topic' (purple button towards the top of page).
This also stumped me for a bit and I reached out to a Shopify Admin for help.