The sweets served with matcha are not a dessert meant to come after the tea. In a traditional tea setting, the usual order is sweets first, then matcha. The sweetness prepares your palate for the bitterness and astringency of the tea, helping the flavor of the matcha stand out more clearly.
The reason makes sense, but it is rarely something people stop to think about while having matcha and wagashi. Eating the sweet first and drinking the matcha afterward simply feels like the normal way to enjoy them together.
When the sweet arrives before the tea, people usually do not wonder whether they are supposed to wait. If you think of it as dessert, eating all of it first can look a little backward. In a tea setting, though, that is exactly the right order.
Wagashi also brings something beyond sweetness. Sweets served with tea are often chosen to reflect the season, using their color, shape, or name to suggest things such as cherry blossoms or autumn leaves. The sweet is part of how the season is brought into the tea setting, not just something used to soften the bitterness of the matcha.
For many Japanese people, there is no need to stop and ask why the sweet comes first. Once the wagashi is served, eating it before the matcha simply feels natural.