There is a encyclopedia in Sanahtlig's toolbox now. Current estimate for Gaia is very early October.Well, the rough dates are late October, mid-April and late March. You have like six months between Tyr and Ares, which is almost enough for the Shards just from weeklies. You also have six months to gather Shards through Ragnarok advents, raid and union events will also give you one or two here and there... and if you can kill Ultimate Advents with just R hime, one per Advent there too (starting from early November).
So, if that's all you need to Awaken and you'll be ready for Tyr, you probably will be able to Awaken all three just fine. Maybe. I can't be bothered to check do you actually get 60 Shards in time. If not, you just need to score first in the first competitive Union fight, late April! That's 15 ez Shards right there!