It really depends how often you're publishing but it's not unrealistic to expect growth within 2-3 weeks. We recommend that you do not significantly exceed your existing publishing speed on your website. If you publish one blog a month right now, we recommend you start with maybe one blog a week. If you're doing one a week already or more, then you can start there and take it up a notch, and then continue to take that up over time.
If you're someone who has been consistently blogging weekly or multiple times a week, it's safe to assume that you could probably very quickly add on higher volume. Maybe you could do two or three a week to start, or more; it's up to you, depending on how you want to run your content system.