Can I get HttpServletRequest instance during application startup
When the application is starting there are no HTTP servlet requests yet. In fact, Tomcat during bootup starts listening and accepting connections on 8080 port, but passes them to appropriate servlets only when all applications have successfully started. This means you cannot call yourself during startup since this will lead to deadlock - you are waiting for a response which is blocked by Tomcat that waits for you.
This also means that it is simply impossible (at least when Tomcat is taken as an exmaple) to obtain any HTTP servlet request during startup as there are absolutely no requests yet. Yes, mocking is the correct way, but I'm afraid if these libraries require an HttpServletRequest instance, simple mock might not be enough.