When was Jesus the Son of God? (Romans 1:4)

The allegation is that Paul says Jesus was appointed the Son of God by the resurrection, therefore he wasn’t before. Here is the verse:

⁴ who was declared to be the Son of God with power, according to the spirit of holiness, by the resurrection from the dead; even Jesus Christ our Lord, Romans 1:4 (ASV)

Let’s start with “by”. The word is actually ἐκ, which usually means “out of, ” but it is strange to use in English that way. “by” is a possibility and seems to work here. I’ve heard someone try to use “at” here; that is also possible. https://www.perseus.tufts.edu/hopper/morph?l=ek&la=greek#lexicon

Now “declared”. This is where most of the problems come in. The idea is that the word should be “appoint” (which some translations say) and therefore he was not this before. The word is ὁρισθέντος. https://www.perseus.tufts.edu/hopper/morph?l=%E1%BD%81%CF%81%CE%B9%CF%83%CE%B8%CE%AD%CE%BD%CF%84%CE%BF%CF%82&la=greek#lexicon

In general terms, it means to “divide” or “set boundaries”. Possible translations are “appoint” or “determine”. This doesn’t quite match with the above “declare”, but consider that one of the things that “declare” can mean is “to fix conclusively or authoritatively” https://www.merriam-webster.com/dictionary/determine and it’s not so off as a possibility.

So we have 2 ways to understand this. He was either appointed the Son of God at this time, or was conclusively fixed as such (as in if Him coming back from the dead isn’t going to prove it to you, nothing else will). So does this verse say the former? Only if you take a strict view that Paul means it this way and is willing to contradict himself in Philippians 2.