Assuming you get all the items via the normal methods (i.e. farming, raising animals, fishing, etc.), the earliest you can complete all the bundles in the community center is Summer 10 Year 2 (or Summer 6 Year 2 if you have Agriculturist + Deluxe Speed Gro). This date is the earliest you can grow a Red Cabbage, which is the latest required item for a bundle.
However, there are several ways to speed up this timeline:
The Traveling Cart, which sells a random assortment of foods and seeds throughout the year. It is possible to buy a lot of otherwise time-gated requirements) from the lady in the cart. She appears on Fridays and Sundays in a clearing west of Marnie's ranch (close to the entrance to the Secret Woods). Keep in mind that she charges a pretty big markup on items.
Once you earn 25,000 total gold, Demetrius will stop by and offer to set up your cave as a research area. He will let you decide whether to study fruit bats (who will leave random fruit on the floor) or mushrooms (which grow random mushrooms). Personally I think the fruit bats are more useful for completing the bundles, but both options are helpful.
The Stardrop Saloon has a chance of selling Maki Rolls, which are needed for the Chef's Bundle on the Bulletin Board.
Once you unlock the Greenhouse (earliest Fall Year 1), you can start growing any crops you might have missed in earlier seasons, if you have leftover seeds. This might save a season or two of waiting.
If you get really lucky, you could theoretically complete the community center in Winter of Year 1 (or maybe even Fall, if you're insanely lucky).
Here's the earliest you can complete each bundle without using any of the above tips:
Crafts Room - Winter Year 1
Spring Foraging Bundle - All items can be found by foraging in Spring Year 1.
Summer Foraging Bundle. - All items can be found by foraging in Summer Year 1.
Fall Foraging Bundle - All items can be found by foraging in Fall Year 1.
Winter Foraging Bundle - All items can be found by foraging in Winter Year 1.
Construction Bundle - Depends on how quickly you upgrade your axe so you can chop the large stumps to get hardwood. Can usually be achieved by late Spring Year 1.
Exotic Foraging Bundle - This bundle requires 5 out of 9 options. Maple Syrup, Oak Resin, and Pine Tar are really easy to get as they only require a tapper. Cave carrots are also super common in the mines. For the last item, you can either look for a red/purple mushroom in the mines, or upgrade your axe twice and hope to find a morel mushroom in the Secret Woods before the end of the first Spring. Either way, this can be completed Spring Year 1.
Pantry - Fall Year 1
Spring Crops Bundle - All items can be grown in Spring Year 1.
Summer Crops Bundle - All items can be grown in Summer Year 1.
Fall Crops Bundle - All items can be grown in Fall Year 1.
Quality Crops Bundle - Requires 3 of 4 options. Since melons and corn are both available in Summer, this bundle can be completed Summer Year 1, though you have more chances to complete in Fall if you don't grow enough gold quality crops.
Animal Bundle - Depends entirely on when you have enough money to start animal farming. Theoretically you can complete it in Spring Year 1, though Summer or Fall is probably more realistic.
Artisan Bundle - Requires 6 out of 12 options. Most of the available options are fruit, which can be acquired with fruit trees. Cloth is easy to get (recycle newspaper) and honey/jam is also relatively simple, so this can be completed by Summer Year 1 if you manage your money well.
Fish Tank - Fall Year 1
River Fish Bundle - You're limited by the Tiger Trout, which only starts appearing in Fall Year 1.
Lake Fish Bundle - Sturgeon are the limiting fish in this bundle, so you cannot complete it until Summer Year 1.
Ocean Fish Bundle - The fish you need don't start appearing until Summer Year 1.
Night Fishing Bundle - Walleye don't show up until Fall Year 1.
Crab Pot Bundle - You need 5 out of 10 options. All options can be caught in any season, and I believe some can be foraged on the beach as well. Theoretically you can finish this in Spring Year 1, though most probably finish in Summer.
Specialty Fish Bundle - There's two limiting factors here - Pufferfish can only be found in Summer, so that's the earliest you can complete the bundle. Sandfish can only be caught in Calico Desert, which is inaccessible until you finish the Vault (costs 42,500 gp in total). Though you can theoretically finish this bundle in Summer Year 1, many people don't have enough money to complete the Vault until at least Fall.
Boiler Room - Spring/Summer Year 1
Blacksmith's Bundle - Requires gold ore, which you can either buy directly from Clint or find in the mines at level 80+. Theoretically completeable in Spring Year 1.
Geologist's Bundle - Fire Quartz can only be found in the mines at layers 80-120, so it takes a while to work your way down there. Theoretically you can complete this in Spring 1, though Summer is more likely.
Adventurer's Bundle - Void Essence is dropped by Shadow Brutes on floors 80+, so again, you can theoretically complete this in Spring Year 1 but Summer is more likely.
Bulletin Board - Summer Year 2
Chef's Bundle - You learn how to make Maki Rolls on Summer 21 Year 1, so that's the absolute earliest you can complete this bundle. However since it requires truffles (which requires a Deluxe Barn for pigs, plus the cost of the pig itself), many people don't manage to complete this until Fall Year 1 or Spring Year 2.
Dye Bundle - The red cabbage is the main limiting factor here, as it is only available Summer Year 2.
Field Research Bundle - The Nautilus shell can only be found by foraging on the beach in Winter, so Winter Year 1 is the earliest this bundle can be completed.
Fodder Bundle - Apples are the hardest part of this bundle to come by, but as long as you've grown an apple tree, you can complete this in Fall Year 1.
Enchanter's Bundle - Pomegranates are only available in the Fall, so that's when this bundle can be completed (Year 1).
Vault - Varies
All Bundles - These bundles are cash only, so the only limiting factor is how much money you have. Theoretically you could complete these by Spring Year 1, but that's pretty unrealistic. I think most people finish this by late Summer/early Fall, or possibly even Winter Year 1.