Wifi network option is not showing up
Troubleshooting is a process of elimination and often requires quite a bit of patience. Let's proceed as follows.

Have you followed Allan's advice?

I'm assuming you've already booted into Safe Mode and used Apple Hardware Test (as suggested by Allan in his comment on May 11)? 


If you haven't, then please follow the steps below for booting into Safe Mode and Running Apple Hardware Test.
If you have, can you please edit your question to provide the results of performing both actions. Then skip the steps below for performing these actions and try the Terminal commands I suggest.


Run Apple Hardware Test


Shut down your Mac
Restart your Mac
Press and hold the D key before the gray startup screen appears.
After a while, Apple Hardware Test (AHT) will start.
When prompted, select your language and click the right arrow. 
When the AHT console appears, you can choose to run Basic tests by clicking the Test button. However, I suggest you select the "Perform extended testing" checkbox before you click the Test button.
Your test results will appear in the window in the bottom-right of the console.


Take a note of the result and report back.

Note 1: The extended test will take some time. Take a note of the results and report back. 

Note 2: If pressing and holding the D key at Step 3 doesn't work, start again at Step 1 and, at Step 3 press and hold both the OptionD keys instead. This will try and run diagnostics from the internet instead, so you will need to allow more time for it to complete.

Boot into Safe Mode

Follow these steps to boot your Mac into Safe Mode:


Fully shut down your Mac
Restart your Mac
Immediately press the Shift key and keep it down 
Let go of the Shift key when you see the login window (NOTE: If you have FileVault enabled you may need to log in twice).
Take a note of what happens (i.e. do you see the Wi-Fi option in System Preferences > Network?)
Exit Safe Mode by restarting your Mac as normal
Check System Preferences > Network again


Once you've booted into Safe Mode, let us know how you went.

Now, assuming you still have the problem after already booting into Safe Mode and running Apple Hardware Test, let's proceed with the following course of action.

Run these Terminal commands

Let's confirm what macOS believes the status of your Wi-Fi service is. To do this:


Launch Terminal
Enter the following command:

sudo networksetup -listallnetworkservices
Press Enter
Enter your password (note you will not see the cursor move, nor the characters appear on the screen)


Now, in the list that appears I assume you will see an asterisk (*) next to the Wi-Fi service. This denotes that it is currently disabled. Assuming this is what happens, let's try enabling it as follows:


Make sure you're still in Terminal
Enter the following command:

networksetup -setnetworkserviceenabled Wi-Fi on
A popup will prompt you for your password - enter it and click on the Modify Configuration button 
Now enter this command:

networksetup -setairportpower en0 on
Restart your Mac
Now check System Preferences > Network again


Let me know how you go.