You can always compete by offering something your competitor does not provide (either different products, different services, different prices, or different target market). Start by finding out what your customer needs - then build a version of your product. Iterate, iterate, and iterate.

If you are only competing on cost, you'll lose every time. Find some other value proposition to compete on like incredible features, fanatical support or something your competitors simply can't do with their outsourced teams.

I can offer the validation steps to see if what you are intending to do will work:

1. Are your / your competitors customers willing to pay a premium for resources that have extensive experience?

if not, then

2. Do you still make enough money to support the business by hiring more expensive experienced employees and offer the product/service at the same price as the competitors?

or
3. Would you be able to offer something more than your competitors that they cannot because they have offshore resources that the customers value and will be willing to pay more?

If the answer to any of the three question above is a firm "YES" you have a chance of winning the market. Else, you should go with the same delivery strategy as your competitors.

The only glitch is, once the competitors start seeing you win in the market and because they are potentially sitting on more cash than you they may catch up pretty quickly to delivering from on shore resources.

Build a great community around you, your users. In this way your users will help to promote and sell you and your product. Maybe you understand your users better than your competitors who are overseas. Can you play on that theme, show your users how you are different and unique. How you help them and go over and beyond each day to grow your company into something bigger that serves them.

The great thing about growing your company online; is that great stories well told by small disruptors with vision, can out-preform and outsell the bigger folks.

You right now are small and agile. This is a strength. You don't have to wait for decisions to be made. You make them. I always think of Giacomo Guilizzoni founder of Balsamiq Studios. He was so open about what he was trying to build, how big his company was (just him) and his vision. His users loved what he was doing so much they supported him in the early days and now Balsamiq is standard for wireframes and prototyping in the industry.

I suppose it is time to think about what you can do and put less focus into thinking about the others. Small can be great and punch well above our weight category and win.Good luck!

Karan's answer is definitely in the direction I would recommend heading.

Except for the most commoditized markets (ie: phone service, purified water, car tires, etc), there's always an angle to take to go up-market. It requires you to improve your messaging and closing skills (or conversion funnel), but it's definitely worth the investment.

Two books come to mind that are really great at unlocking ventures from the low-price trap:

1. Blue Ocean Strategy: This is a very thorough study on differentiating and the step-by-step process to identifying the variables to focus on to really stand out. It's so good that I used it as the textbook for a semester-long feasibility class at Fresno State.

2. Pitch Anything: This helps you frame your offering in a way that's compelling and not battling over the lowest common denominator items the market thinks are important.

Obviously, this is very general since the market and business model is unknown at this point, so feel free to follow up with any clarifying questions.