Quite a question, opens up issues of freshness and sometimes desirable aging. Sometimes fresh is not best, oolong and Gyokuro are often best aged ... and this subjective when is it "best" can vary from person to person, not to mention vendor to vendor.
If you are buying direct from country of origin, vendors will generally show harvest info. Or for instance if it is new harvest aka "shincha." A lot of greens/new harvest teas from japan and China start to come to market in March (I am not too keen on super early Chinese green which are way overpriced IMHO), April, and May. However, this does not mean you cannot buy a very good sencha for instance right now. As long as the vendor is properly handling, packaging, and storing their teas, it is no problem to get good sencha any time of the year. Similarly with Chinese green teas. Even some Chinese and Japanese greens are subjectively better with a little aging. Shincha is not always best for everyone ... for every tea!
The road gets more bumpy from here on though as you start to consider other types of teas such as oolong and black as well as domestic (USA) vendors. Generally, USA vendors are a few months behind country of origin vendors due to shipping and buying considerations. You need to ask the vendor if they are not disclosing this info on their site. IMHO, I think all vendors should disclose this info, but instead, USDA and/or FDA regulations only require that they readily offer expiration info. I am not too keen on subjectively assigned expiration dates.
Show me the harvest info!!!!
Oolong and Black ... another post ...