It could mean just what is says: God was manifest in the flesh.
It shows here the it was the 'son of God' who was manifest is the flesh.
[ 8 The one who practices sin originates with the Devil, because the Devil has been sinning from the beginning. For this purpose the Son of God was made manifest, to break up the works of the Devil.]
[14 So the Word became flesh and resided among us, and we had a view of his glory, a glory such as belongs to an only-begotten son from a father; and he was full of divine favor and truth.]
'God' there is referring to Jehovah. 'Son' there is referring to Jesus. Jesus (the word) is the one who was made manifest in the flesh.
Even if 1 Timothy 3:16 said "god' and not 'he', that would not mean that 'god' there is referring to Jehovah God. 1 John 3:8 and John 1:14 makes clear that it is Jesus (the word) the 'son of God' is who was made manifest in the flesh.
The reason it could have said 'god' even though referring to Jesus is because Jesus is also said to be a 'god'. Again though, that does not make him Jehovah God, just like Satan is said to be a 'god' and yet you do not claim he is Jehovah God.