Green Bacon is fresh and cured bacon that has not been smoked or aged further. Hot smoked meat does not last as long and the fat of hot smoked meats can go rancid. This led many recipes of the time to not include smoking bacon. At the very most, cold smoking was recommended. Your average chef in the 1600's is not going to take the additional step if it means the food won't be preserved as well.

The Closet of Sir Kenelm Digby Knight (1669) bacon recipe suggests smoking as an option but goes out of the way to say that the smoking should be very light if done or else the bacon will spoil.

then take it out, and wipe it dry, and hang it in a room, where they keep fire, either on a hearth, or that smoak cometh out of a stove into the room (as most of those rooms do smoak) but hang them not in the Chimney, that the hot smoak striketh upon them; but if you have a very large Chimney, hang them pretty high and aside, that the smoak may not come full upon them. After a while, (when they are dry) take them thence, and hang them from the smoak in a dry warm room. When the weather groweth warm as in May, there will drop from them a kinde of melted oyly grease, and they will heat, and grow resty, if not remedied.

Bacon was a staple in the diet of England through the centuries. The meat was also very important in ship rations in the 1500s. Older recipes as found in Le Menagier de Paris don't mention smoking at all and instead focus only on the curing and use of salt. The good Huswifes Handmaide for the Kitchin put out in 1597 suggests to dry cured bacon near a fire but does not say to smoke it.

This doesn't mean that smoking was never done to bacon, as it did enhance the flavor. Smoking was typically for those of a higher class who could afford the extra cost in the food preparation and did not have to worry about rationing or preserving their food.

Sources:
Defeat of the Armada by Laughton

The Closet of Sir Kenelm Digby Knight

The good Huswifes Handmaide for the Kitchin