How to effectively share knowledge about a product across all team members

I work as a software developer for an outsourcing company and started working for a recently bought startup. The codebase is spaghetti and it’s very hard to understand how the whole thing works. The bigger problem is that there’s absolutely no documentation. My team struggles to understand both the code and the product as a whole.

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The guys who created the product want to improve it. It looks like that they really want to get us up to speed but we still haven’t found a way to effectively share knowledge about the product. We have regular meetings which we call office hours where everyone can ask questions which has arisen in the process of working on tasks. The problem with this approach is that there’s a time difference and while waiting for answers one is not optimally productive.

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Are there other ways to effectively share knowledge about a product across all team members that you’ve experienced or read about?