Minimum 6 months
FICO starts scoring after there are at least 6 payment entries in your credit report. This means 6 months at least, maybe a few more because it takes time for the credit card companies to report your activity to the credit bureaus, and some more time for them to update their data base.
Vantage score starts scoring immediately, but don’t wast your time or money on it.
Although the three major credit bureaus try to push it very hard, the plain truth is that most banks and credit card companies use the FICO score (around 90% of them use FICO), so there is no point checking your Vantage score.
FICO and Vantage use different scale and formulas, so you can’t guess your FICO from your Vantage and vise versa.
P.S. there is a free KreditKarma score (and a few others), but again – no financial institution uses them.