THIS QUESTION HAS BEEN ASKED AND ANSWERED MANY, MANY TIMES AND IS PART OF THE DATABASE.
CORRECTLY USING THE SYSTEM WOULD HAVE PROVIDED THE ANSWER WITHOUT ANY DELAY or inconvenience of others. There are also several discussions about what those claims of early filing/early refund really are and what they mean.
There is no fixed date, but you cannot file until you have all your forms (paystub DOES NOT QUALIFY). And of course, filing before the IRS really has the departments staffed that handle the filings, won't mean anything happens with it.
You really can't even try to file until February 15th. Prior to that date you must make every reasonable effort to obtain a W-2 from your employer. who is required to mail or otherwise deliver your W-2 to you no later than January 31st. Not receiving a W-2, or any form for that matter, does not excuse you from reporting that information on your return..but not having them will delay processing.
Also, you need any of the other forms (like 1099, from banks, etc), and if you do file
with out them, there are additional forms you need to provide so the IRS can find out why whoever was to provide them didn't. Obviously this can delay the processing of your return. and if the amounts you showed don't exactly match what is filed (and employers frequently have some year end changes that will make your last stub in accurate), you would have to file an amended return to correct it. or expect nasty-grams and assessments from the IRS! Certainly no refund will be made until all that is cleared up. so trying to do things other than as the system wants, generally only delays things.
Finally, if your wanting to do so early because you have a large refund coming. especially if that is common for you. you should file a new Form W-9, to change the amount of withholding being done so your not always having too much taken out of your check through the year.
The IRS Tax Calendar at http://www.1040.com/federal-taxes/irs-tax-calendar/ says the earliest date you can file electronically is January 17th and that is also the date of the first IRS acknowledgements of e-filed returns.