It is novel to create a variable for the find so I'm going to offer a more traditional method rather than try to figure out the nuances. It is also odd to dimension the variables repetitively inside a loop. Try this version of your code
Code:
Sub AddHyperlinksToTimeMarkers()
Dim mtgID As String, aRng As Range
Dim hrs As Integer, mins As Integer, secs As Integer, startTime As Long
mtgID = InputBox("Enter meeting ID") ' Ask for meeting ID
' Find all six-digit numbers (time markers)
Set aRng = ActiveDocument.Range
With aRng.Find
.ClearFormatting
.Text = "[0-9]{6}"
.MatchWildcards = True
' Loop through each time marker and add hyperlink
Do While .Execute
' Get hours, minutes, and seconds from time marker
hrs = CInt(Left(aRng.Text, 2))
mins = CInt(Mid(aRng.Text, 4, 2))
secs = CInt(Right(aRng.Text, 2))
startTime = hrs * 3600 + mins * 60 + secs ' Calculate starting time
' Add hyperlink to time marker
ActiveDocument.Hyperlinks.Add Anchor:=aRng, Address:="https://ABC?meetingid=" & mtgID & "&start=" & startTime
aRng.Collapse Direction:=wdCollapseEnd
Loop
End With
End Sub