Depending on the rest of your application, if you studied HARD for 2 months you may be able to break 30 on the MCAT. You would have to sign up for a middle June test date and make sure that your primary application is completed exactly 30 days after your MCAT.
This would allow your application to be submitted in the middle of July, which is not 'early', but its not 'late' either. Ideally, you'd want to submit your primary by the middle to end of June for an 'early' app. If you do well on the MCAT, and have a solid app otherwise, submitting your primary by Middle/late July (and also your secondaries very expeditiously) will give you a decent shot for the coming year.
The timeline is this:
End of April:
-Graduate
-Open AMCAS application
-Send transcripts ASAP. It takes AAMC 2-8 weeks to verify your transcripts so get them in as soon as you graduate and your AMCAS file has been created.
-Ask letter writers to be your referees
End of April-June:
- Bust your butt for 1.75 - 2 months for the MCAT and take it in the last week of June.
July:
-While waiting for your MCAT scores bust your butt perfecting your PS and primary application.
-Try and get this submitted by the 3rd week of July as it will take them a few days to 'certify' your application. Your transcripts should already be verified.
-Hopefully by now your LORs are ready and uploaded to interfolio or virtualevals.
Last Days in July:
-Receive your MCAT score and wait for secondaries!
As you can see, the timeline is very tight. Is it doable? Heck yeah it is. Will it be fun? Probably not...but if you don't want to wait I suggest that you attempt this.
Now, the hiccup in this time-line is that it is totally feasible that you may not be ready for the MCAT in 2 months. If that is the case, you'll have to delay your application...at that point you'll have to decide whether you want to continue applying this year or just apply next year.
Don't worry if you have to take a few years off. Some of us start later than others. (I'm 24
)