Most likely the best way to get funded in this situation is to approach independent investors. It would really depend on your business plan and whether or not you have an attractive business model. You could try to get connected with networks or consultants that have access to independent investors such as chambers of commerce, or consulting firms Global Strategy Consulting Services, LLC www.gscsconsulting.com or you could email email@example.com and someone will respond with ideas on how to get you funded.
Residence is not a factor for venture funding -- what's important is building a network so you can get in front of the right people in the US venture community.
Loans for small businesses are really restricted to established businesses with clear cash flow and preferably some obvious assets (like real estate). Most startups can't get a small business loan. Does not matter whether you're a US resident or not.
Also why do you have an LLC? It is the right structure for some companies, but not others.
Happy to discuss further.
If you are trying to raise capital through private financing, the residency of the owner of the LLC is generally not a factor. The larger US bank and financial institutions will have an issue with the LLC being a nonresident. It is easier to borrow funds if the LLC is taxed as a C corporation, or if you setup a traditional corporation rather than a single member LLC.
An SBA loan is the only Traditional business loan option that can work for a new startup opportunity. However, this is a government backed loan and it requires you to have a green card or be a permanent resident, That said, you may have a partner that does have a green card or is a permanent resident own 51% or more of the business, while you own 49% or less ---- in this case, the SBA lenders will make exception for you. The SBA Standard of Operations will allow for this situation to move forward. Alternatively, you may also consider using other means of financing to include: private loans/peer-to-peer lending, home equity lines of credit (be careful how you navigate this though), Retirement 401k type financing (called the Rollover for Business Startup Program), and/or Portfolio Loans if applicable.