I guess my first question is why you would want to do that? If you are creating an LLC, a corporation, or some other legal business entity that you are going to register with the CO Secretary of State, you need to get an employer identification number. However, even sole managers or members of LLCs normally file taxes under their own SSN instead of the EIN. You do not have any employees, serve as an independent contractor, and do not have a business license. So, what is the benefit of getting an EIN?
If you are operating a business under your own name or an assumed name ("doing business as" or d/b/a) you generally would use your own social security number for tax purposes. Even if you set up a limited liability company (LLC), if you are the only member, the entity is disregarded for tax purposes and if you have no employees, you still would use you own SSN. Whether or not you have a business license is a matter of local law and does not affect your tax status or what ID number you use for tax purposes.
This response contains general information only and is not legal advice on which you may rely. It does not establish an attorney-client relationship.
It is legal to apply for an EIN when you don't have a business license and don't have any employees. Many businesses start by getting an EIN and forming a company, and then get a business license. And there are many businesses with no employees other than the owner of the company.
As well, business licenses are local issues - whether you need one or not depends on the city or county where you are running your business. The EIN is a tax issue - it relates to your status with the IRS (and the state for state income tax purposes). The IRS is not going to care if you have a business license or not and the city or county likely won't care if you have an EIN or not.
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