Most men try to make themselves look good in the beginning of a relationship.
Most men put on a good show when they first start dating a woman.
この場合、次のような言い方ができますよ。
ーMost men try to make themselves look good in the beginning of a relationship.
「ほとんどの男性は、恋愛関係の初めに自分を良く見せようと頑張る」
to try to make themselves look good で「自分を良く見せようと頑張る」
ーMost men put on a good show when they first start dating a woman.
「ほとんどの男性は、女性と付き合い始めに、格好良く見せようとする」
to put on a good show で「格好良く見せようとする」
例:
Most men try their best to put on a good show when they first start dating a woman, but their faults get exposed after a while.
「ほとんどの男性は、女性と付き合い始めに、格好良く見せようと頑張るが、しばらくするとボロが出る」
one's faults get exposed で「ボロが出る」と表現できます。
ご参考まで!