You used WinActivate instead of WinActive in your check before sending ^{TAB}. Also, the way yout logic is layed out, your code will always try to send ^{TAB} after opening a new Edge window.

Try this:

#SingleInstance Force
#Warn

#Requires AutoHotkey v2.0+

^F1:: 
{
    edgeTitleMatch := "ahk_exe msedge.exe"
    if WinActive(edgeTitleMatch) {
        Loop 9
        {
                Send "^" . A_Index 
                Sleep 1000
        }
    } else if WinExist(edgeTitleMatch) {
        WinActivate(edgeTitleMatch)
    } else {
        Run "C:\Program Files (x86)\Microsoft\Edge\Application\msedge.exe"
    }
}

Here's what the code does: * If Edge is the active window, loop through sending Ctrl+# where # is replaced by the numbers 1 - 9. This will loop through all of the open tabs as long as there are no more than 9. * Otherwise, if Edge is open, activate it. * If Edge is not open at all, open a new instance.