Look around your neighborhood, especially if you live in zone 5.
Do you see any trees blooming in June?
You do if someone has a Japanese Tree Lilac (Syringa reticulata 'Ivory Silk') in their garden.
I don't know why more people don't plant this small tree, as it provides a flush of bloom in early June (in my garden) at just about the same time as the many shrub type lilacs are a pleasant memory.
It has a sweet scent but I have to get right up next to the flowers to smell it, whereas lilacs like Syringa patula 'Miss Kim' flood the entire yard with scent in May when they are in bloom.
The tree lilac's one flaw in my garden is that it really has no fall leaf color to speak of, or at least not that you would notice when compared to a tree like a red maple.
You most likely won't find these trees at big box stores. To get a Japanese Tree Lilac, you should go to a good garden center or nursery. And try to get a named variety like 'Ivory Silk'.