Blaze a trail
To lead the way.
When soldiers 'blaze away' with their weapons the blaze refers to the fire and smoke. This has been used since the late 18th century, as here from the Battle of Brooklyn, 1776:
"We bid them stand and blazed away like brave boys."
The meaning we now give to 'blaze a trail' - of someone forging ahead and clearing a path for others, would tend to lead towards imagining blaze to mean burn, in the same way. Another allusion might be to someone charging ahead with such vigour that they leave a smoldering trail in their wake.
Those aren't the thoughts in the mind of those that coined this phrase though. A blaze is a notch or mark, like the blaze marks seen on horses' faces. So, 'to blaze a trail' was to mark it out by notching trees so that others could follow. Trees are also often marked this way to single them out for felling.
The use of blaze to mean the chipping off of a small piece of bark to mark a path or boundary is American in origin. That's seen in these early citations.
Dr. Thomas Walker's Journal of Exploration [of Kentucky], 1750:
"I Blazed a way from our House to the River." & "I blazed several trees in the fork and marked T. W. on a Sycamore Tree"
John J. Henry's An accurate account of the hardships of that band of heroes who traversed the wilderness in the campaign against Quebec in 1775:
"A path tolerably distinct, which we made more so by blazing the trees."
The first actual usage of the precise phrase 'blaze a trail' that I can find is from the Montana newspaper The Helena Independent, November 1883:
"The merchants thereupon, desirous of securing the trade of the new mines, offered the stranger $100 if he would blaze a trail through, and afterward it could be cleared sufficiently for pack animals to pass along."
See other phrases that were coined in the USA.