Is it possible to call TBB processing a component within a page at the time of publishing the page itself (with the subsequent replacement of a component with a component that has been processed TBB)?
Yes, it is possible. Publishing itself is a multi-stage process.
The first stage is Resolving: this is where a class adds/removes/edits publish items to the publish Package, you would implement a Customer Resolver class to do this (see https://docs.sdl.com/LiveContent/content/en-US/SDL%20Tridion%20Sites-v2/GUID-F792AB1A-060A-4757-802D-3A2DB18F022D).
The second stage is Rendering. This is where TBBs come into play and do their thing.
Another way you can manipulate publishing, is by adding actions to publish events via the Event System.
Hope this helps is what you're trying to accomplish. Best bet is to get into Visual Studio and start working with the APIs. If you've already done that, let us know what code you've tried and where you're stuck and we can help with the specifics.