The coast of North America north of 45 degrees north was unknown, and there was the great, undefined, and imaginary southern Continent to disprove.
Whether other voyages of exploration would have been undertaken one cannot say; but in 1768 the Royal Society put in a word.
A transit of Venus over the sun's disc was to occur in 1769, and astronomers were anxious to take advantage of it, the object of the observation being to ascertain the distance of the earth from the sun, the fundamental base line in all astronomical measurements, and which was very imperfectly known.
The Central Pacific afforded a favourable position, and the Royal Society memorialised the king to send a ship for the purpose.

The request was granted, and at first Alexander Dalrymple, who had conducted marine surveys in the East Indies, and was known as a scientific geographer, was selected as observer.

As, however, it was found that he also expected to command the ship, the Admiralty positively refused to have anything to do with him, and after some discussion James Cook was selected.
This says volumes for Cook's reputation at the time.

To have risen absolutely from the ranks was a great deal, but to be chosen as a master, to command a ship, and undertake a scientific observation of this importance, was a most exceptional occurrence, and speaks well for the judgment of those who had the selection.
It seems that Mr.Stephens, the Secretary to the Admiralty, had much to do with it.

How Stephens had become acquainted with Cook history does not relate, but doubtless his personal visits to the Admiralty in connection with the completion of his charts of Newfoundland, from which he returned every winter, had brought him into contact with the Secretary, who had clearly formed a high opinion of him.
Cook, we may be sure, jumped at the chance, and his pride must have been great when he found he was to receive a commission as Lieutenant.
This in itself was a most unusual step.