Ah, but you can, for a while anyway. The first few dates are usually one-on-ones, so no need to show that you have a vast social network. Then you could say that you just moved to the area and don't know anyone yet. Or you could BS and say that your friends are busy/out of town/working for the Red Cross in Timbuktu when your new partner asks about them. These are only temporary "fixes" though.

If you have agoraphobia on the other hand, this can be concealed indefinitely. Going out to crowded places may cause discomfort and anxiety but it can be hidden.