Consider this answer an extended comment, subject to deletion or removal to History.
The short answer to the main question is no, as far as we know there was never any consideration of synchronizing the Thanksgiving holiday with the advent season. At the same time, we should be aware that the origin of Thanksgiving is based entirely on Christian sentiments of prayerfulness, and was originally as much a religious holiday as the annual day of prayer .
The other answers have answered the question well and given a bit of the history of the Thanksgiving celebration. There is some confusion about the dates of celebration though. The dates of the celebration, at least since it became a regular event in 1863,seem to have been either the last Thursday in November (usually the fourth, but sometimes the fifth); the fourth Thursday in November, or (actual celebration or only proposed?) the third Thursday in November.
In 1863, at a time of national crisis, President Lincoln proclaimed Thanksgiving, which previously had been celebrated in some places, a national holiday according to this article:
On the urging of poet and magazine editor Sarah Josepha Hale, the 16th president took what had been a festival celebrated disparately across the country and made it a national holiday, to be observed on the last Thursday of November. (In 1939, President Franklin D. Roosevelt would move it to the fourth Thursday of the month.)
This article adds some more details. President George Washington had declared the nation's first Thanksgiving in 1789. Since that time many states and organizations had celebrated Thanksgiving, but not on a national basis. Lincoln himself had closed government offices for a thanksgiving celebration on November 28, 1861.
The full text of Lincoln's proclamation is at that page. Notice that it sets the date, "the last Thursday of November next", setting a precedent which was apparently followed without much objection until 1933, when merchants desired more shopping days until Christmas.
History.com gives many more details about Thanksgiving. The holiday originated in 1621 when the Pilgrims gave thanks to God for their survival and the help of Native Americans, who apparently brought most of the food. A Thanksgiving was celebrated again in 1623 after fasting for relief of drought. Fasting and Thanksgiving became a common but irregular custom thereafter.
During the American Revolution, the Continental Congress designated one or more days of thanksgiving a year, and in 1789 George Washington issued the first Thanksgiving proclamation by the national government of the United States; in it, he called upon Americans to express their gratitude for the happy conclusion to the country’s war of independence and the successful ratification of the U.S. Constitution. His successors John Adams and James Madison also designated days of thanks during their presidencies.
Apparently President Franklin Roosevelt resisted the request to change the date of Thanksgiving in 1933, but in 1939 the history.com article claims he "moved it up a week", which I assume meant it would be the second-to-last week in November; usually the third but sometimes the fourth Thursday.
... [in] 1939, ... Franklin D. Roosevelt moved the holiday up a week in an attempt to spur retail sales during the Great Depression. Roosevelt’s plan, known derisively as Franksgiving, was met with passionate opposition, and in 1941 the president reluctantly signed a bill making Thanksgiving the fourth Thursday in November.
Note: I ask your indulgence in not upvoting nor downvoting this until we figure out where or if this belongs. My apologies for getting carried away and forgetting this is not a Wikipedia article.