I should throw my experience in here. I was at 9K before my current job. I came into a company that was doing quick upgrades to anyone who qualified. I was thinking I'd get about 100 hours in the jet and upgrade. During my new hire time, they put a company policy in place that anyone without prior turbine experience, you had to have 300 with the company prior to upgrade. I got my 300 hours but missed the last upgrade class I could hold by about a month. Upgrades slowed for a while. I ended up with about 1,200 in the right seat before upgrade. In hindsight, I'm a better pilot and captain for it.
Even if they're offering it, I'd suggest getting a couple hundred hours in the right seat of a jet before upgrade if you can.