Psalms 127:2 It is vain for you to rise up early, to sit up late, to eat the bread of sorrows: for so he giveth his beloved sleep.
This is an example where rising up early is motivated by obsession for monetary gain or something to that extent, so it is a bad thing, or staying late, probably to worry from how it's worded. The Psalmist talks completely differently when the staying late and rising early is to spend time with God in "night watches". So it shouldn't be taken that literal rising up early is necessarily a godly thing, and vice versa. Seems it's bad if you're being too wrapped up with daily life and concerns.
When you pull "early" thought out the Bible, you find that "rising early" also packs spiritual meaning, besides expounding wisdom on practical living like Proverbs:
Psalms 57:8 Awake up, my glory; awake, psaltery and harp: I myself will awake early.
Sin is compared in the Bible to drunken stupor, sleep and slumber. Repentance from sin and being mindful of God is like waking up from that unresponsive slumber. The Bible is using these things from physical life as examples to illustrate spiritual life. Waking up early has to do being spiritually awake and alive, to reality of God, and unto God. "Early" could be taken in that meaning as "without tarrying, now, quickly" or "fervently, earnestly". Such as we can draw from the context here with much more certainty:
Proverbs 8:17 I love them that love me; and those that seek me early shall find me.
It's obviously not about praying at 4am, but that a fervent seeker of God is a guaranteed winner. A fervent seeker is bound to have an intense prayer life, though. I would contest that "early" here is not about time of the day, and that God is telling us something else here.
Mark 14:37 And he cometh, and findeth them sleeping, and saith unto Peter, Simon, sleepest thou? couldest not thou watch one hour? 38 Watch ye and pray, lest ye enter into temptation. The spirit truly is ready, but the flesh is weak.
Revelation 16:15 Behold, I come as a thief. Blessed is he that watcheth, and keepeth his garments,(...)