Paidon is correct.
"Only begotten" does not mean "only one of a kind, or unique." It absolutely requires the concept of "begetting" (procreation). I know some modern translations translate John 1:18 as "unique" but this can easily be shown to be false. For example:
Luke 7:12 NKJV "And when He came near the gate of the city, behold, a dead man was being carried out, the only son [μονογενὴς] of his mother;and she was a widow. And a large crowd from the city was with her."
The literal rendering would be: "behold, one having died was being carried out, the only-begotten son to his mother;"
Now, try seeing if it makes any sense translating it as unique: "behold, one having died was being carried out, the UNIQUE son of his mother"
If you use the word "unique" it implies she had more sons, but this one was somehow different. That is absurd in this context, since the whole reason Jesus had compassion on her was because she was left with no children.
The LXX makes it quite clear that this word means "only begotten" not "unique."
Judges 11:34 "And Jephthae came to Massepha to his house; and behold, his daughter came forth to meet him with timbrels and dances; and she was his only-begotten, he had not another son or daughter. The second clause lays stress on the one before it. Note that both the concept of "only" (he had no other = mono-) and "she was his daughter," thus begotten = geneao). There is nothing implied about uniqueness in these passages or any other.
All of the older English translations translate it as "only-begotten." I have also found ECF quotes which use this term, and their argument absolutely depends on it meaning "begotten" not "kind." The only reason some modern scholarship says it means "one of a kind" is because of their bias against what the Bible teaches about Christ being God's "only-begotten Son." When they can't get their theology to work in certain passages, they change the meaning of a key word to make it work.
Monogenes is not used in the Bible (LXX or NT) in any way other than an "only-begotten" child. The usage of μονογενὴς in John 1:14:
Καὶ ὁ λόγος σὰρξ ἐγένετο καὶ ἐσκήνωσεν ἐν ἡμῖν, καὶ ἐθεασάμεθα τὴν δόξαν αὐτοῦ, δόξαν ὡς μονογενοῦς παρὰ πατρός "only-begotten from the Father."
This was the first time John used μονογενὴς and it establishes an important precedent. John did NOT modify the noun υἱός (Son) with the adjective μονογενὴς as he did elsewhere. Instead, he used μονογενὴς as a substantive. Whenever an adjective is used as a substantive (without modifying any noun), the meaning contained in the adjective is sufficient so that no noun is needed. However, in this case, since μονογενὴς stands on its own without modifying any noun, no class, kind, or category is provided in which to understand "only" or "unique" (if either of those was in fact its meaning). Unless it means "only-begotten" it makes no sense in this verse. If μονογενὴς merely means "only" or "unique," then the question in the mind of the reader would be "ONLY WHAT?" or "UNIQUE WHAT?" A class, category, or kind is demanded in order to distinguish the sense of the substantive. The adjective alone would not provide category, class, or kind, in order to understand what the writer meant. However, if μονογενὴς means "only-begotten," then using this adjective as a substantive is perfectly natural, because it inherently requires having been procreated -- an only-child.
Paul uses "monogenes" in Heb. 11:17 BECAUSE in Gen. 22:2 God called Isaac Abraham's ONLY son, using the word אֶת־יְחִֽידְךָ֤ which means SOLITARY (not one of a kind). The LXX reads differently here, saying: λαβὲ τὸν υἱόν σου τὸν ἀγαπητόν ὃν ἠγάπησας τὸν Ισαακ "Take the son of you, the beloved one, whom you loved, Isaac."
However, if you look at the very next verse, Heb. 11:18, it explains WHY Isaac was called by God Abraham's "only-begotten."
Hebrews 11:17: By faith Abraham, when he was tested, offered up Isaac, and he who had received the promises offered up his only begotten son, 18 of whom it was said, "In Isaac your seed shall be called,"
That means God was not going to reckon Ishmael as "Abraham's seed" from His perspective, even though he was Abraham's seed literally.
The reason modern scholars get this wrong is because they do not understand the Abrahamic Covenant. They look at the Scriptures through the eyes of Ishmael and Mohammed instead of through the eyes of Isaac and Paul. So, instead of having their eyes opened here, they take their faulty assumptions, change the meaning of the word "monogenes" in order to accommodate their error, and then use that new definition to interpret John 1:18 so they can prop up the Alexandrian Text reading which refers to the Son as "monogenes God" instead of the majority reading "monogenes Son."