There is no such thing as "activating" a green card. Only US permanent residents can have a green card, and you do not become a US permanent resident until you enter the US with your immigrant visa. It sounds like what you have is just a US immigrant visa, and you do not have a green card.
When you enter the US with your immigrant visa, you will become a US permanent resident, and the Green Card Test will apply, which will make you a resident alien for tax purposes, and thus subject to US tax on your worldwide income. However, (assuming you haven't been to the US much in the years before) since you only became a resident alien this year, the First Year of Residency rules apply, which means that you are only considered a resident alien for only the part of the year after you became a permanent resident (if you meet the Green Card Test) or the part of the year after you were first present in the US this year (if you meet the Substantial Presence Test), whichever is first (if you meet both tests); and you will be considered a nonresident alien before that, so you will be a dual-status alien for the year. If entering the US with your immigrant visa is the first time you are to the US this year, then the time before that, you are a nonresident alien, and you are not subject to US taxes on non-US income during that time.