QUESTION: How long after I have my H1B can my employer file for the Green Card? 

ANSWER: The simple answer is at any time. Clearly, there is a misunderstanding here.  The H1B and the Green Card are completely separate processes.  One has nothing to do with the other.  But, one process does complement the another.  We will get to that later.

If you are on OPT/STEM OPT/CPT or just an F-1 student or maintaining some other lawful status in the U.S., your employer can start the green card process for you. There is no requirement that you must be working on a work visa, such as the H-1B or L-1A, with your employer in order for your employer to sponsor you for the green card process.  For the most part, a person gets an offer for the green card process once they have worked for the employer in some capacity. Some of the employers that I represented over the years have done the green card process for people who work in their offices overseas because those employees are so vital to business and those companies wish to retain that talent. In other cases, I have run through the entire green card process (labor certification, I-140, and I-485) for beneficiaries that were on OPT/STEM OPT. They never even got to the H1B. Instead they got their green card. Again, the motivation by these employers was to make sure that they retain talent. If you can go through the entire green card process while a person is on OPT/STEM OPT, then that means they are from a country of chargeability that is not subject to per country limitations, i.e. quotas on the number of visas issued for that country per year. 

But, if you are from India, China, Philippines, Mexico, El Salvador, Honduras and Guatemala, then you will not be able to complete the entire green card process in one shot because of current backlogs in the EB2 and EB3 visa categories. These countries are subject to quotas due to the amount of immigration that these countries have to the U.S. So if you are from one of these few countries, in order to adjust status from whatever status you hold to a green card, you will need to maintain a status in the U.S. for a significant period of time or return home. In most cases, if you are from one of those visa backlogged countries, your employer will simultaneously register a case for the H1B lottery each year, while the first two steps of the green card process are pending. This is because they obviously want to keep you here and have you work for them while the green card process is pending. Once your labor certification is approved and your I-140 is also approved, and you have also secured your H-1B, then in that circumstance, you have essentially solidified a path to the green card that will allow you to remain in the U.S. by seeking successive extensions from USCIS of your H-1B visa until you are able to adjust status. Pursuant to the American Competitiveness in the Twenty-First Century Act of 2000 (AC21), with regulations published on January 17, 2017, under section 104(c), an H-1B visa holder is able to request 3-year extensions of their H-1B beyond the normal 6-year limit of the H-1B visa, if they have an approved I-140. This extension is available to beneficiaries present in the U.S. and those abroad. This is where the H1B complements the green card process. One (the H-1B) is necessary for the other (green card process) to get to the adjustment of status stage to get to the actual green card.  By having an approved I-140, the H-1B can be extended for how ever long it takes for your priority date to become current so that you can apply for adjustment of status. Again, this would only apply to beneficiaries who are subject to per country limitations, such as those countries listed above.