How to install MacOS into new SSD

Using the built-in Internet Recovery Mode (macOS Utilities menu) you don't need to create your own bootable installer in order to install a fresh macOS onto your new SSD.

The best way to do this is to boot up into Internet Recovery Mode on your MacBook Pro after you have installed the new SSD by holding either SHIFT-OPTION-COMMAND-R (if that works), otherwise OPTION-COMMAND-R.

How to reinstall macOS from macOS Recovery - Apple Support

Then, go into Disk Utility and erase your drive as either an APFS or HFS+ (Mac OS Extended) partition.

How to erase a disk for Mac - Apple Support

Then quit Disk Utility and select Reinstall macOS from the Utilities menu.

MacOS from app store does not download as a standard download.

If you download the OS from the App Store, you aren't getting a standalone installer? What do you get when you download the OS?

You can make a bootable USB stick to install using these free programs which will do all the work for you.

Bootable USB Flash Drive – Diskmaker X      Disk Creator   or use Apple’s method       Create a bootable installer for OS

When you are looking for Mojave, you should download the full installer, approx 6.1GB.

In the Appstore: Lately it should download the full installer (instead of the starter only).

When you are looking for an earlier MacOs (ElCapitan and older), that you had on your Mac:

Log in in Appstore, Go to the "purchased" tab, redownload.

For Sierra: https://support.apple.com/en-us/HT208202

For HighSierra: https://itunes.apple.com/us/app/macos-high-sierra/id1246284741?ls=1&mt=12

Try the links below.

Check the computer requirements shown in each link to see if your computer is capable of running that OS version.

How to upgrade to macOS Mojave - Apple Support

How to get macOS High Sierra   

Sierra download

You can try to download it at the link below. If it won't let you, then your only options are to upgrade to Sierra/High Sierra/Mojave or find an older computer where you can download it using your Apple ID.

El Capitan

You could have no hard drive/SSD in your system and Internet Recovery should still load.

Since it's not loading the next thing to look at is a network issue. The best thing to try would be a friend's home/residential Wi-Fi other than your own because there may be something about the Internet connection you are using that's blocking access to Apple's recovery server.

If you have a built-in ethernet port you can try that as well by plugging into your router, as not doing Wi-Fi eliminates a lot of (but not all) potential Internet issues. And if that doesn't work, a friend's router.

Do you have access to another computer where you could sign into the App Store using your Apple ID to download the installer. You could then make a bootable USB. See the links above for download assistance.