So, you ask, can I go from a smaller firm to Big Law eventually (assuming that is a goal)? Yes, you can. But how? Well, wherever you are, you want to do great work and build your reputation. Get involved in bar activities (you can often get involved even as a law student). Reach out to potential mentors. Offer to assist with committee work such as newsletters or meeting preparation. Yes, it is grunt work and takes up time you could be doing other things, but it is a great long term investment. Get your name out in the community. Work in an area you love (ok, at least like). Try to develop sub-specialties in growing areas. When recruiters call you, be polite -- call them back and establish a relationship. If they don't call, ask friends for recommendations and reach out.
Where does Big Law come in? Well, a couple (few?) years down the road, slots will open when associates depart through the normal course or an area picks up and the firm needs additional bodies. Firms will reach out further to fill these slots. I have recommended several candidates we interviewed from smaller firms because of the experience in a certain specialty area where we needed help.
Familiar tune here? HP hopes I don't sound like a broken record when HP says that you need to push forward even harder during more difficult times to build your reputation, network, and seek opportunities.
More on connecting with the small and mid sized in a later post.