Push-ups and abs?

Good afternoon. I’ve been putting in work with push-ups and sit-ups for about four days now. I’ve heard through the grapevine that these are the gold standard for building a solid physique, and since I’m currently in that prime growth phase—fifteen years old, standing 6'0", and weighing about 143 lbs—I’m curious about the timeline. Realistically, how many days or months will it take before I actually start seeing the fruits of this labor? Thanks in advance!

You’ll likely see some actual progress in about three weeks or so

You're looking way too thin... nothing to show for it. You need to eat, and a lot more than you currently are.
How many sets are you actually running, and what's the rep count per set?
You should be hitting various abdominal movements—standard crunches, leg raises, side planks... variety matters.
Wide-grip pushups target the chest, whereas those narrow ones—the kind the Marines use—are better for your triceps and forearms. When you do them, try aiming for ten reps per set.
One more thing; I know this guy in Chicago, he's 35, and he cranks out 600 pushups every single day in sets of 50. Honestly? The guy isn't strong at all. If you saw him shirtless, you wouldn't think twice about his physique. The point is, muscles eventually hit a plateau... if you just keep doing the same thing over and over, they won't grow. If you actually want some mass, you need to join a gym and lift heavy.
And yeah, hanging from a pull-up bar... that’s solid work.