Go talk to people. Right away. If that works you want as much overlap with the departing person as possible.
The people to start with are your direct manager and the leaving architect. The architect is really good choice, since they have no more personal interest in the game an can you give objective advise and fit assessment.
Your boss is always your first address for all things career related. Ideally you should have regular career development discussions with your boss anyway and this opportunity would just be an extension of this discussion.
If these two discussions go well, next step would be to approach the architect's manager or whoever makes the hiring decision and would be your new boss (if different from your current one).
If the previous discussion do NOT go well, you need to analyze why and adjust accordingly. For example: if both the architect and your boss feel you are missing a key skill (either technical, behavioral, or organizational), then you should probably let this one go and create a plan close the skill gap.