There is no such thing as a global trademark. There are trademarks in different countries, and when you start doing business in those countries you can file to obtain a trademark in those countries.
For example, Ivanka Trump's fashion line had U.S. trademarks and has been in the process of obtaining Chinese trademarks over the last few years since she has started doing business in China.
There is no particular timeline for obtaining a trademark. Simply using it gives rise to common law trademark rights without any filing in many countries in the places and markets where you use it, and you can't obtain a trademark until you are using it in commerce in a country or imminently about to do so.
But, unlike a patent which goes into the public domain if you don't timely perfect it with a patent filing, a trademark can be obtained at any time before someone else is granted the same trademark in the some geographic area in which you seek one, in the market for goods or services of the same type as you are seeking.