The relevant rules text:
An alchemist begins play with two 1st level formulae of his choice, plus a number of additional forumlae equal to his Intelligence modifier.
Unlike a wizard's starting spells text ("The wizard also selects a number of additional 1st-level spells equal to his Intelligence modifier to add to the spellbook.") the alchemist class write-up doesn't strictly mention that the extra formulae from high intelligence have to be 1st-level spells.
So my question: Can a hypothetical 20-int alchemist (+5 modifier) start play with 5 first-level extract formulae known (2 from base features and 3 from int mod) and 2 second-level extract formulae known (from the remainder of the int mod)? Obviously, he wouldn't be able to actually brew the second-level extracts until level 4, but could he have the two of them in his formula book from the get-go?
Yes, but given how relatively chap and easy it is to scribe formulae I would generally recommend picking up ones that are actually usable at first level and by the time 4th level rolls around you should have more than enough resources to buy a couple of extra formulae.
This advice of course goes out the window if the GM/campaign in question is unusually restrictive about access to other spellcasters willing to share their knowledge for profit.