Most large aircraft these days take off with close to full power (surprisingly, rarely AT full power), with partial flaps extended and wheels down of course. They climb fairly steeply at a lowish speed to reduce the amount of noise on the ground (noise footprint area). Then they “clean up” the aircraft, wheels up, flaps up and reduce the climb rate (put the nose down a bit) and reduce power to the max continuous climb power setting.
The normal process for the take off goes something like this …
Pilot flying will push the thrust levers forward to establish take off thrust. He’s looking forwards, out the window. The pilot monitoring will call “power set” and place his hands behind the other pilots hands to make sure the thrust levers don’t move. The pilot monitoring will call the increasing speeds “80 knots” so the pilot flying knows the aircraft is accelerating nicely and the flying controls will now have full authority, the the pilot monitoring calls “V1” (the stop or go speed) and shortly after “Rotate” when the aircraft reaches the VR (velocity rotate) speed. The pilot flying pulls back on the stick or yoke, and lifts the nose. The aircraft continues to accelerate as it lifts off. The pilot monitoring calls “positive rate” (the aircraft is climbing properly), and then pilot flying will, when ready, call “wheels up” which the pilot monitoring does, and then calls “wheels up” to confirm they are retracted. The aircraft continues to accelerate and the pilot flying calls “flaps 5”, then “flaps up” (or whatever settings are used for that particular aircraft) once the aircraft has accelerated to a safe “flaps up” speed. The pilot monitoring mives the flap lever and confirms that instruction. That will happen before the aircraft reaches about 250 knots (most large aircraft have a flaps and wheels down limit of something like 250 knots). The nose is then dropped to accelerate the aircraft to its climb speed of somewhere between about 280 and 340 knots depending on the aircraft and any ATC separation requirements, and the thrust levers are set to the climb power. Of course they also follow their departure clearance from ATC regarding turning on to their departure heading or towards a particular navigation aid.
That’s a rough outline of the process.
If you are sitting near or over the wing, and depending on the aircraft, you can usually hear the thumps as the wheels come up, and then the wheel doors close (B737 don’t actually have wheel doors – the wheels just tuck snuggly into recesses in the wing root but you can still see them). And shortly after that you can see the flaps retracting into the wing, and might even hear the rrr-rrr-rrr sound of the jack screws spinning as they wind those flaps in.
That “putting the nose down a bit” can feel like it’s descending, but it’s just changing the body angle to get the aircraft accelerated to its most efficient climb speed to suit the long climb (20 minutes or so) up to cruising altitude. At the same time the engine thrust is reduced to the climb thrust setting which reduces the “push in the back” you get during the take off. That combination of slightly reduced thrust and the nose up angle reducing can certainly feel like it’s descending for a moment, but it’s definitely not slowing or descending – that’s just a body perception.