When you throw an asteroid at a planet, you don't actually throw the asteroid. You modify its orbit so that it intersects the planet.
Modifying orbits is not a game of changing the position of an asteroid as much as it is a matter of applying delta-v. This is good news to your story, because it means that the effort required to make a 100x larger asteroid hit a planet takes about 100x as long, not 10x as long as you might expect from naive $d = \frac{1}{2} a t^2 + v t$ mathematics.
Fine-tuning it well enough to hit an actual city is extremely difficult computationally. On the other hand, super-efficient and slow asteroid manipulation is also extremely expensive computationally.
The most efficient way to make an asteroid hit the Earth is make other celestial bodies do the work for you. At the most naive, you apply delta-v when the asteroid is Aphelion from the Sun, which makes your delta-v more valuable.
But going further than that, you could arrange for your asteroid to approach a planet (or other body) from behind and "sling-shot" around it. This can steal delta-v from the planet and get a change in orbit that is insanely larger than the cost to nudge the asteroid.
This doesn't stop there. You could start playing an insane chaos-monkey game of nudging a tiny asteroid that nudges other asteroids positions, that eventually gets one of them chaotically to move closer to a minor planet like Ceres, which in turn causes other bodies to shift.
A scout ship with a ridiculously insane (almost magical) ability to compute could use extremely small amounts of energy and large amounts of chaos to cause asteroids to start intersecting the target planet's orbit.
There are situations where making an asteroid hit a planet is a matter of a small thrust and lots of time. That is when the asteroid or other body is already almost hitting the planet. But almost all of such asteroids are relatively tiny, the timing of the hits isn't inside the scout ship's control, and the ship won't be able to pick a dino-killer "off the menu".
As a bit of a frame challenge, the sensible way to do interstellar colonization or conquest is by using star wisp Von Neumann machines.
Here you have a very tiny seed ship you launch over interstellar distances using something like a solar sail and launch laser. Then you repeat the process, much more difficult, using two solar sails to come to a halt at the target system.
(Your tiny payload has a large solar sail. You fire a laser at the large solar sail, which you detach from the payload. The payload deploys a small solar sail,and uses the reflected light to brake and approach the target system.)
The goal is to have as much of the infrastructure to travel interstellar distances in the launching system, where you have the energy budget of a K1 or K2 civilization to play with, and as little as possible within the "space ship" as possible. Interstellar distances are very long.
Once you reach the target system, you start working on the long, slow process of reproduction of your Von Neumann machine.
Imagine that machine has a production capacity of X, and it takes 1000 years for the machine to double that production capacity. Then after 10,000 years you'll have 1000x the capacity, 20,000 years 1 million times the capacity, 30,000 years 1 billion times the capacity, 40,000 years 1 trillion times the capacity, 50,000 years 10^12 times the capacity, etc.
If you can double your production capacity and sustain that over many many repetitions, the time it takes you to do the doubling isn't as important as the fact you can double in the first place. After well under 100 doublings, you are a K2 civilization, and have consumed the entire solar system's resources.
Such an exponential process is extremely slow to "get off the ground". A civilization that threatens to reach the space age within a few thousand years is thus a serious threat. Once they are in space, they could work out how the Von Neumann machine works, and with the higher production capacity of a populated world outpace it. Even before they reach space, observation of the Von Neumann machines using astronomy could clue them in, and accelerate their technological progress.
A "hostile" source of such reproducing probes could result, and an entire chunk of the galaxy could be lost to the colonization effort.
At the same time, the energy budget they can afford to spend on actually interfering with the ground-based biomatter is limited, as the Von Neumann machine requires most of its budget to keep up the exponential reproduction cycle.
And growth is the purpose of the probe. The driving goal is to build a new lauch site, and send out another 10 probes. This may take 100,000 years, but the probe and its sisters together will claim the entire galaxy in a blink of an eye this way.
If every 100,000 years, 20% of probes launched succeed and produce an average of 10 probe launches, after 1 million years each probe launched causes 1000 launches, on the time scale of millions of years the Von Neumann probe-front is a relativistic phenomena, limited by the speed of the probe flight, and not by reproduction rate. If the probes travel at 0.0001c (extremely fast really), the wave crosses the galaxy in 500 million years; mostly leap-frogging, where probes are launched "behind" the front wave, and the front wave mostly is in charge of firing braking lasers.
Further from the front wave, the Von Neumann machines stop their obsessive probe launching, and print out a civilization on the colonized systems. These civilizations do whatever they want; they can do science, art, whatever. Some may work on optimizing the Von Neumann probe system, improving probe speed, reproduction rate, or whatever (note, however, that this becomes an information security problem; compromising the reproduction network of probes is an easy way to take control of the galaxy and mold it in your own image).
So under this model, the "scout" probe is attacking the planet using extremely low-hanging asteroid fruit, because it (a) really doesn't want them advancing to the space age in the next few kiloyears, and (b) is really busy trying to boot strap itself to the point where it doesn't care what the planet does.
It requires 10s of thousands of years for plan (b) to take effect. If the planet does advance to the space age, it can get help from other systems at a high cost. A nearby system could, for example, convert their entire star into a huge laser and fry this system's main planet's biosphere from interstellar distances. This is not 100% reliable, and failure results in a guaranteed of an extremely hostile civilization with access to Von Neumann probe technology. Also, it destroys the system that fired the laser (the probe-civilization has a lot of systems; cauterizing one to get rid of a potential danger is expensive, but not unheard of).