Nope. You don't have the prerequisites for it.
A bombing alchemist can benefit a great deal from taking point blank shot and precise shot at level 1 (assuming you're human) and precise bombs at level 2.
You cannot take the extra discovery feat until you have an actual discovery. It's determined by level.
When do I count as having a class feature?
You have a class feature when your class description tells you you gain that class feature, generally based on your level in that class (and perhaps altered by factors, see below).
If you have an archetype or other rules element that replaces that class feature, you do not have that class feature. For example, if your archetype replaces a rogue's sneak attack, you no longer have the sneak attack class feature (whether a requirement is as general as "sneak attack" or as specific as "sneak attack +1d6," you do not qualify for it).
If you have an archetype or other rules element that replaces part of a scaling class feature, or delays when you get that class feature, you do not have that class feature until you actually gain that class feature.
Example: If you have a fighter archetype that replaces weapon training 1 (but not weapon training 2, 3, and 4), you don't gain the weapon training 2 ability until fighter level 9, which means you don't have the weapon training class ability at all until you reach fighter level 9. Anything with "weapon training" or "weapon training class feature" as a prerequisite is unavailable to you until level 9.
Example: If you have a cleric archetype that replaces channel energy at level 1 (but not later increments of channel energy), you don't gain the channel energy ability until cleric level 3, which means you don't have the channel energy class feature until you reach cleric level 3. Anything with "channel energy" or "channel energy class feature" as a prerequisite is unavailable to you until level 3.
Example: If you have a witch archetype that replaces your hex at level 1 (but not later hexes, major hexes, or grand hexes), you don't gain your first hex ability until witch level 2, which means you don't have the hex class feature until you reach witch level 2. Anything with "hex" or "hex class feature" as a prerequisite is unavailable to you until level 2.
You gain your first discovery at level 2, and that's when you're considered as having the Discovery class feature. You cannot take extra discovery feat until you're level 3.
There is the option of retraining at level 2 though hey?
Yes, in theory you could retrain once you get to level 2. It would cost you 10 x your lvl x days of retraining in gp cost and 8 hours of uninterrupted training. So 8 hours, and 20gp. Your GM has to be cool with it as well though, obviously.
Five years.
Five years.
Did anyone else read this in the voice of "Finish Him" from Mortal Kombat?