Some skeptics charge Jesus with missing out on Elijah being first to “ascend into heaven” but the solution is the same as it is today: The Hebrew word translated “heaven” in the first verse. shamiyim, simply means the sky, as “heavens” does metaphorically today. The “heavens” were also regarded as the abode of God, but at the time of 2 Kings there was as yet no conception of “Heaven” with a capital H as the special abode of God shared with His people.
The Greek word in the second verse, ouranos, can also mean the sky, but it is also used in the sense of God’s realm (as in, the “Kingdom of Heaven” [ouranos]. Note John 3:27 “John answered and said, A man can receive nothing, except it be given him from heaven.” The word carries theological freight that shamiyim does not. Therefore, there is no conflict in these verses, for 2 Kings merely asserts where Elijah went physically and carries no theological overtones. (read more here)