Try it now: Tap your hand on the desk randomly. Can you recall how many times you did it without "saying" a sequence in your head like "1, 2, 3" or "A, B, C" etc?
If yes, how far can you count? With a language it's effectively infinite. You could theoretically go up to "1 million 5 hundred 43 thousand, 2 hundred and 10" and effortlessly know what comes next.
If I want to translate this knowledge into a number, I need to count the taps I am seeing in my head. At that point I do need to think of the word for the number.
I could even do computations on these items in my mind, imagine dividing them into two groups for instance, without ever having to link them to words until I am ready to do something with the result, such as write down the number of items in each group.