I agree. If you're using this
Double Pitch pack, then you're starting with 200 billion cells which should be more than enough to direct pitch.
If you just want to make a starter for the fun of it, then you can use 1000mL (~33floz) with 100g (~3.5oz) of DME which will fill up about half of your growler. (It's roughly the same amount you originally posted, and will work just fine to use 4 cups water with 1 cup DME.) I used growlers for a while before I had an Erlenmeyer flask and stir plate and they work just fine. You definitely don't have to worry about the large head space, and you don't want to fill it up all the way because you'll lose a lot out the top. Just give it a swirl whenever you walk by it.
Here's the problem: His wort is 1.070, not 1.060 or less. So he does not have enough viable cells to direct-pitch. It says right on the product page that you are looking for .75 million cells per milliliter of wort per degree Plato. For reference, 5 gallons is 18,927.1 milliliters, and 1.070 SG is 17 degrees Plato.
Let's do the math:
18,927.1 mL * .75 = 14,195.325 Million cells per degree Plato
14,195.325 / 1,000 = 14.195325 Billion cells per degree Plato
14.195325 * 17 degree Plato = 241.320525 Billion cells needed for 5 gallons of 1.070 wort
Now, a new yeast pack contains ~200 billion viable cells, and they start dying eventually (the rate of death is debatable and variable, but we won't get into that here). So we can assume that, at most, we have ~200 billion viable cells, and most likely there are fewer than that. Using a best case scenario, we are ~41 billion cells short, which is about 17% of the total number of cells needed for this fermentation.
All of that to say that it can probably still be done, but you will be substantially short of your typical ideal pitching rate for ales. In some styles of beer, this might actually be desirable, but in a style where you are seeking a clean fermentation, it is not.