Aurora R9, HDMI or DP for Sceptre monitor

If your CPU support graphics then connector marked (on a picture below) as Red-A (DP / Display Port, would require DP-to-HDMI adapter in your case)
If you prefer to use add-on GPU (and assuming it works) then Blue-B (DVI) or Green-C.
Also depends on what is selected in your BIOS as primary adapter (but BIOS can be reset to use default settings if you just got this PC from a second-hand market).

In Windows once it's loaded it might have it's own configuration what monitors are enabled or if in use (and detect newly connected monitor automatically in most cases, although hot-plugging monitor connection is not normally a best practice),
but during boot it should show you logo and probably some technical info on a monitor what it detects as main video output for PC.

Since monitors are sometimes slow with detecting what input has signal (but PC checks if there's device connected on another end of a video cable) and in some cases doesn't switch between inputs automatically - it might need manual selection right before powering PC on and without much of a delay (to prevent monitor going into automatic detection attempt on a different input because PC might decide what there's no receiver on another end of a cable). This is why manual mode is preferred in some unusual cases.

Sometimes windows might be configured to use unsupported resolution by monitor, or refresh rate - ending with no visible output on monitor.

If add-on Discrete GPU is faulty (the one with connectors B & C) - then it's highly recommended to remove it from PC.

P.S. there are no hidden ports related to video output for user to connect monitor to in default  Aurora R9 configuration.

For high end gaming monitor such as Sceptre Monitor I would suggest use DP port of discrete graphics card to connect to monitor DP port.  the onboard DP integrated gpu has much slower speed compared to discrete gpu.

See the technical specifications on how to connect a display to your R9: R9 technical specifications 

Please note the following:

- The Display Port at the back panel cannot be used, so don't try to use it as it will not operate.

- Pending on the video card that was supplied with the system, the available ports might look different than the picture from the technical specifications manual.

I should also add that a "fast connection" is dependent on the type and version of the connector used. It looks, based on the picture, that your video card only has HDMI and DVI-D out. Without knowing the model of the graphics card it's hard to say what version of HDMI it supports, but if you are looking at a high refresh rate display I am afraid you are more than likely out of luck and stuck to 60 Hz at 1080P.

it looks like vanadiel is probably correct as there is no Intel Multi Display option mentioned in R9 system set up options aka BIOS.  this may suggest the presence of discrete gpu would disable the integrated onboard gpu.  Dell normally ships it with the onboard DP port covered as a reminder to user not to use it if unit is shipped with a video card.  I think they are probably all shipped with a discrete card.  R9 video spec is all about a discrete card.  

use onboard DP only when you suspect the discrete card has issue and you would remove it to make sure motherboard itself has good POST.  in other words the onboard DP is good for diagnosis only not meant for regular use (although it is permissble.).

Would have to provide a picture of the connectors on the video card to make sure of the available connectors. Hard to see in the supplied picture.

The regular 1650 would just have DVI-D and HDMI, while the 1650 Super has that + a DP port.

Graphic cards for Alienware desktops 

HDMI 2.0b limitations:

While HDMI 2.0b can support 4K resolution, it can only do so at a maximum frame rate of 60Hz. In order to reach 120Hz and 144Hz, a display’s resolution must be dropped down to around 1440p (Quad HD) or 1080p (Full HD).

DP 1.4 limitations:

DisplayPort 1.4 has a maximum total bandwidth of 32.4 Gbps and a maximum total data rate of 25.92 Gbps. That gives it support for the High Bit Rate 3 (HBR3) mode, which opens up a wide range of resolutions and refresh rates. Along with support for 5K resolutions at up to 60Hz, and 4K resolution at up to 120Hz, DisplayPort 1.4 can handle 240Hz on both 1080p and 1440p resolutions

So always use the DP connection, if your video card has one.

This is OP's video card.

3NR1F

CRD,GRPHC,NV,GTX,1650

 

GTX1650 is 700% faster than integrated UHD630 of i7-9700k of R9.

 

Can you help with where the discrete graphic card is?  

Also the monitor sadly does not have a DP, just HDMI.

Thanks so much, I am SO not sure -- and got this computer as a gift without a manual etc.  

What would you suggest -- which cables and where to connect based on the picture?

So many thanks.

That Aurora R9 shipped from Dell September 2019 with the following added discrete video card =
3NR1F Nvidia GeForce GTX 1650 4GB, HDMI 2.0b, DVI-I

In your picture, you are already plugged into the lower on the tower discrete (added) GTX 1650 graphic card HDMI out port.

The top DP video out port was turned off when the discrete (added) GTX 1650 graphic card was installed.

Your monitor only has HDMI in ports. If you remove the discrete (added) GTX 1650 graphic card from the tower, you could then connect to the top DP out port on the tower to the monitor via a DP to HDMI cable.

Thanks so much, and sadly I am not under warranty.  Would there be any way for you to send me a picture of what you think is the best?  (So appreciating the help!)

Dell Chris is right. Just to illustrate where the discrete card is, it is the one add-in card that has hdmi cable with blue tag plugged in

Chris M below suggests (I suspect as part of automatic signature):
[...If still under warranty, click the "Get help now"...]

But service-tag check returns warranty status as: "Expired 29 SEP 2021"

That is indeed where I have mine plugged in!  So that's the correct and fastest one for my monitor in your opinion?

And on the monitor, is it HDMI 2 I imagine?