You join a team with no test process at all. What do you do in the first month?
First find out where quality actually hurts: talk to support, read the last three months of incidents, ask developers what they are afraid to touch. Then fix the cheapest thing with the biggest effect, usually a smoke suite on the critical path plus a bug workflow people follow. Writing a test strategy document in week one is the classic mistake — nobody reads it, and you have not earned the credibility for it yet.