You should be able to create a session for a newly created user and redirect your anonymous user to your homepage with the right cookies for your newly created user to kick in.
Something like what I have below:
ISession session = Core.initializeSession(user, null);
response.addCookie(XAS_SESSION_ID, session.getId().toString(), "/", "", -1);
response.addCookie(XAS_ID, "0." + Core.getXASId(), "/", "", -1);
response.addCookie(OriginURI, OriginURIValue, "/", "", SECONDS_PER_YEAR);
response.setStatus(HttpServletResponse.SC_SEE_OTHER);
response.addHeader("location", indexpage);
If you're using the OAuth 2.0 module, it already has this in it.