Does the text here (Gen 4:3, 6) imply that Cain and Abel lived in or near the presence of the Lord? How is this possible?

Yes. They do not offer on an altar; they brought their offerings “unto the Lord.” Moreover, when the Lord “had not respect” for Cain, he is immediately aware of it, meaning the Lord must have done, or failed to do, something to indicate his displeasure. Finally, we have the Lord in direct conversation with Cain, and the matter is definitively settled with “Cain went out from the presence of the Lord” (Gen 4:16). They did not live in the Garden, although they might well have lived east of the Garden while still in the land of Eden. When Cain is sent away, he goes to a different land, Nod, and so presumably not in a visiting distance of God. What is interesting here is that the Garden thus might have resembled in function the Holy of Holies of a temple, which Cain and Abel might approach, and out of which they might hear the voice of the Lord. It is probably no accident that the future tabernacle, and even more the various temples were decorated in ways that resembled the Garden—even down to the cherubim protecting the Holy of Holies.