This is completely up to you. You can argue that their technology has some insane radiation output, finding them by random chance or them wanting and being capable of hiding themselves from humans. Please don't use sound though. Just through visibility alone, it's a stretch though. Please also note that whatever they emit that we detect has also to travel a great distance. We will not detect any ftl particles and interpret them correctly in 1 week since we do not have any instruments that do that. I'd ask a different question: how do we detect them? What sort of radiation is a good candidate?

When you say 'beyond Pluto' what are your outer boundaries? The Kuiper Belt ? The Ort Cloud? The distinction is important because Pluto's orbits about 30 AU from the Sun (Earth s orbit is 1 AU). The Kuiper Belt extends out from that to about 50 AU. The Ort Cloud is thought to extend from 2000 to 5000 AU! Where they 'drop' into the solar system effects the distance they are from Earth (and given your one week time limit) the speed they have to travel to get here afterwards.

If they can't use FTL travel in the solar system due to gravity perhaps it would be easier for them to enter well off from the plane of the ecliptic from the direction of one of the suns poles perhaps. Also if using FTL travel we won't be able to pick up anything until they arrive.

Just say that your FTL is affected by a star's mass and it has to show up a certain distance away from it. The combined mass of the planets is essentially a rounding error, by comparison.

Need more info for a real answer. Do they want to be noticed, or are they trying to hide? What sort of "noise" do they produce? A brief light flash might go undetected, something like a fast radio burst probably would be en.wikipedia.org/wiki/Fast_radio_burst A gravitational wave burst would be if the detectors are on-line...

How much energy (and what type of energy) is released when they arrive? How big physically are the ships? How many ships are there? After exiting FTL, are they at a dead-stop standstill, and have to accelerate to get to Earth?

Something I'm unclear on: is it one week from when we (on Earth) detect signals of the aliens' arrival in the solar system to when the aliens actually get to Earth? Or is it supposed to be one week from when we detect the aliens' presence to the time that they arrive in the solar system?

@jamesqf, They are not trying to hide, the "noise" is anything that works for the story, I get the idea. But like I said I only want an end goal and the means can be anything. The answers below covered that pretty well.

@cowlinator, Just enough to be noticed by us, any type of energy even multiple types as they have problems. They are around a kilometer in length, stuff like mass effect only different. Yes after the FTL jump they arrive at a dead stop and have to even wait a while for the FTL drives to recharge. They have to accelerate to go anywhere after the FTL jump.

@DavidZ, Arrival. Basically once they arrive they emit all sorts of energy, have not decided on the exact type yet, and we detect that right away

@Mon, Honestly I did not think of a particular boundary. I guess that's such a small thing at this point that I might just ignore it for now. But excellent point. Thanks for point that out.

Seallussus. The thing is light takes about 4.5 hours to travel between Pluto & Earth. So if they arrive just beyond the the Kuiper Belt they're more than 7.5 light hours away. If they arrive just inside the inner edge of the Ort Cloud? Roughly 12 and half days!!! So if you want them to be approaching Earth (i.e about to enter orbit) in just 7 days they will either have to emerge from their 'jump' at a very high velocity inbound on exactly the right vector or be capable of very high Delta Vs to accel & then decel in time. Even Pluto's distance might be pushing it if the limit has to be 7 days.

@Mon, They have FTL ships. Arriving in earth within a week should be fine. This is also a part of the whole FTL travel in the world. The more you want to jump closer to planets the more resources you have to expend. BUT non FTL travel is much cheaper with less resources so the fleet utilize that. So their ships can reach great speeds outside of FTL without much resources. So it is a matter of economy after all.

‘Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.‘

When you say “ Humans need to find out about them. One week in advance.”, do you mean a lot of humans, as in it’s news headlines, or can it be a handful of scientists who have a weird idea about the strange phenomenon that their instruments have detected and might start to write a paper about it in a few more weeks?

If they do not care about being notices by other races, maybe their ships just send out radio-beacons (like planes at the night sky have visible lights) so different fleets of the aliens can see each other? If each ship sends out a strong, sharp regular radio signal, someone will probably pick it up on earth?

Space is 3d but your images show that the Solar System is not (that much): the major planets' orbits are all within a +- 6° inclination of the same plane. Minors like Pluto, Ceres, Pallas and Vesta incline more, but contribute a miniscule amount of mass to the solar system. See @Slarty 's comment above.

A week in advance of the drop from FTL, or a week in advance of their arrival on Earth? The former would be problematic -- the signal would have to reach us before they did, which means that it would have to travel even faster than their FTL.

There's a fundamental problem with the premise that they have to stop beyond Pluto: The Solar System is quite flat. If they were to take a different approach vector, they could get far closer to Earth without stopping beyond Pluto. BUT. If it's mass that wreaks havoc, then they might have to stop a certain distance from the Sun (and Jupiter), in which case the approach vector wouldn't matter.

Frame challenge: With the best current Earth technology it takes half a day just to get to the moon, and just Mars is more than 100x farther even at its closest approach to Earth. If the aliens are prevented from using exotic technology, "a week away" is likely already on top of us from an astronomy perspective. Detecting something that's a bit past the moon is an entirely different kind of task from detecting something out by Pluto. Why not just have them be detected when closer?