This is what “interpretation” of Scripture (Hermeneutics) does.

The verse goes “literally” as:

“And the angel said to them, Fear not: for behold, I bring you good tidings of great joy which shall be to all people.” (Luke 2:10)

The way all “error of the wicked” is developed to their “destruction”: They will claim that “all people” is “not all people” or “believers only” or “made available to all people” etc; “none” of which is “written in the Bible” (thus it’s a man-made error – this false interpretation).

Fact is, “nothing” can stop the Living God to Save “all” people as this is the “Good News” as other “verses” Testify too:

“… God is the Saviour of all people, especially those who believe.” (1 Timothy 4:10)

Please take note of the phrase “all people” in both verses. And yes, Greek does “not” have the definite article “the” as it is in English; so, “all people” and “all the people” mean the “same”.

Remember, when you “interpret” Scripture against what’s “literally” written, it’s like a man saying, “God didn’t quite use the right words to say this; here it is in better words and hence this is the real meaning”.

Don’t be deceived.
Be wise.