Customers can be very skeptical at times. If they know you have a new business, they may be hesitant to buy from you – this is especially true of businesses that operate only online.
One way to overcome that fear is to research and learn all you can about your products/services – become an expert on what you do. Post articles on your blog about them, or put up an especially good FAQ page to answer questions about your product lines in depth. In a bricks and mortar store, make sure you can speak knowledgeably about what you do.
If the question of how long you’ve been in business should come up, you can then honestly say something like: “I had a special interest in this business for a long time, and I’ve done a lot of research and personal comparison of these products (or services). And a few months ago I finally decided to put all my knowledge to good use and opened the business. I know my product better than anyone!”