Interesting suggestion, but you can't isolate the first line from the rest of "Stopping by Woods on a Snowy Evening."
If it stood by itself, you might be able to support the idea that the speaker is thinking that the woods belong to God, if there is a God, of which the speaker is unsure. However, the second line clearly states "His house is in the village." This certainly sounds like a statement of a specific, known but not present, individual human owner of the woods.
If you were interpreting the "house" as being a church in the village, since churches may be thought of as being houses of God, this would answer that concern. Assuming this is your argument, God in his village house would be able to see the speaker "stopping here To watch his woods fill up with snow", which contradicts the third line of the first stanza.
Faith and doubt don't appear to be considerations in the interpretation of this poem.
I think this line of inquiry is futile. The "owner" whom the speaker (let us call him Robert Frost) refers to has to be a human being, a man at that, since Frost says they are "his" woods, not "hers." There are at least two reasons for thinking that the owner of the woods is human. One is that "His house is in the village." Of course, there must be at least one church in the village, and that could be regarded as God's house, but God has such houses all over the world and isn't confined to that one. Furthermore, Frost says, "He cannot see me stopping here." God is supposedly omniscient and can easily see Frost stopping there if He bothers to look. Why should God care about a man stopping to look at some trees?
Then why is Frost concerned about whether the man who owns these woods might see him? This is a fascinating question which has been discussed ever since the poem was published. I have given my answer in a short essay titled "A 'Criminal Patina' in 'Stopping by Woods on a Snowy Evening'" which is posted in eNotes; see reference link below). Frost specifies that this incident occurs a few days before Christmas, on "the darkest evening of the year." He lived in New Hampshire at the time, and his poem was published in a collection titled New Hampshire. At that time of year, the beginning of winter, the deciduous trees would be bare and not worth stopping to look at. The trees Frost is looking at must be evergreens. These are grown commercially in New Hampshire in particular, for sale in the big Eastern cities as Christmas trees.
Frost is thinking that if the owner saw him sitting there in his sleigh staring at his spruce trees, this tight-fisted Yankee squire would naturally assume that Frost was fixing to cut down one of his trees and take it home for the holidays. That materialistic tree-owner could not think of any other reason why another man would stop to look at a stand of trees when it is snowing--or even when it isn't snowing. The woods filling up with snow can only be a beautiful sight because they are spruce trees with spreading branches that will catch the falling snow and soon be covered in white. (It is quite possible, in fact, that Frost really might have been toying with the idea of taking one of the smaller trees home with him, though he doesn't say so in his poem.)
According to the New Hampshire Christmas Tree Promotion Board:
Christmas trees are grown all over New Hampshire, from the rugged Great North Woods above the White Mountains [where Frost lived for many years] to the scenic Lakes Region, in the pastoral Monadnock area and on to the farms of the Merrimack Valley and the Seacoast. Most of the farms are family owned and operated and range in size from less than an acre to 100 acres in size. The New Hampshire farms grow a number of different species of Christmas trees, although Balsam fir and Fraser fir are the most numerous.