This will probably be the first achievement that you unlock. You can get caps quicker by rushing rooms and sending dwellers out exploring. Be careful not to rush the same room too much within a short space of time as the incident rate will increase! I think that might be help. ENJOY!!!
You will unlock this fairly early in the process of building your vault.
You can help speed up this process by rushing rooms though be careful not to rush the same room multiple times in a short period of time as the incident chance will increase after each rush attempt.