WebDriverException: Message: The browser appears to have exited before we could connect error with GeckoDriver Selenium and Python

This error message...

WebDriverException: Message: The browser appears to have exited before we could connect. 
If you specified a log_file in the FirefoxBinary constructor, check it for details.

...implies that the GeckoDriver was unable to initiate/spawn a new WebBrowser i.e. Firefox Browser session.

You need to take care of a couple of things as follows:

• To set the FirefoxBinary you need to use the FirefoxOptions() and instead of passing the absolute path of geckodriver binary, you have to pass the absolute path of the desired firefox binary.
• As you are using GeckoDriver v0.21.0 you have to mandatorily use marionette so either keep it unchanged (by default true) or set marionette to true.

• Your own code with incorporating the minor changes will be:

  from selenium import webdriver
  from selenium.webdriver.firefox.options import Options
  from selenium.webdriver.common.desired_capabilities import DesiredCapabilities
  
  binary = r'C:\Program Files\Mozilla Firefox\firefox.exe'
  options = Options()
  options.set_headless(headless=True)
  options.binary = binary
  cap = DesiredCapabilities().FIREFOX
  cap["marionette"] = True #optional
  driver = webdriver.Firefox(firefox_options=options, capabilities=cap, executable_path="C:\\Utility\\BrowserDrivers\\geckodriver.exe")
  driver.get("http://google.com/")
  print ("Headless Firefox Initialized")
  driver.quit()
  

• Console Output:

  Headless Firefox Initialized
  

• Here you can find a detailed discussion on Unable to find a matching set of capabilities with selenium 3.4.3, firefox 54.0 and gecko driver 0.17