First - recognize if you can compete on scale alone or not
When competing against a firm that benefits from an advantage such as economies of scale, it is important to recognize whether you would be able to realistically compete with them. In this case, consider whether you will actually be able to achieve the economies of scale that they benefit from. Economies of scale is essentially a volumes game – unless you can achieve the volumes that they have, potentially by pulling away market share from them, then it is going to be difficult to achieve the scale advantages that they benefit from.
Consider alternative approaches to achieving cost leadership
If you are trying to compete on a cost basis against a firm with greater economies of scale, and it is unrealistic that you can match their volumes, then consider if there is an alternative approach that you achieve the cost benefits. For example, is there a way of developing a new product or technology that is substantially cheaper than existing firms. Maybe you can engineer out manufacturing costs at the design stage, allowing you to achieve lower costs, despite not having the scale that they have.
Provided it is difficult for the existing firm to match your new way of competing (e.g., it would be difficult for them to reconfigure their operations), then it is possible that you can undercut their position despite a scale disadvantage. And, if you are able to gradually increase your customer base, you may be able to benefit from increasing scale benefits over time – potentially allowing you to catch up on that dimension, while also having other cost advantages.
Investigate if there is a different way of competing - less on price
While it is possible that you may be able to determine a different approach that allows you to compete on cost despite a smaller scale, you may also determine that achieving such an advantage would be very difficult. If this is the case, consider if there are different dimensions that you can compete on beyond cost. While becoming the lowest cost provider is one way of competing, an alternative approach is to include additional features to try and increase the price that customers are willing to pay beyond the bottom cost-leadership position. Just recognize that going head-to-head on the same dimensions against a firm that is stronger than you is rarely a route to success.