I'm recollecting from my years in grad school in Seattle (1987-1991) when I brewed half a dozen spruce beers. I used to pick them in the Cascades while hiking, typically in June or July. I'm sure their available at sea level much earlier. The crucial thing is they should be soft and bright green compared to the older blue-green growth. If there not still soft, it's too late. I don't know that you can be too early.
Currently On Draft: Bamberger Rauch Dunkel, Belgian Blond, Pilsener Urquell clone, Smoked Porter
Bottled: Concord Pyment, Mi'Apa Sparkling Mead, Chimay Blue, Old Simcoe American Barleywine, Old Cantankerous
Fermenting and Conditioning: Pseudo-Decoction Munich Dunkel, Left Hook Bitter
Recently Kicked Kegs: Fresh Hop Pale Ale, Citra Rye IPA
On Deck: Old Rasputin, Northstar IPA, Ur-bock Dunkel