Well it kind of is. At the 8.58cm^3 I calculated earlier and factoring in that the limit for sphere packing is ~74% efficiency means a thousand marbles takes up 11,595cm^3.
To make that easier to visualize that's 11.6 liters or 3 gallons.
For comparison the capacities of a a couple (only ones I could find with volumes listed) of sling bags from Amazon:
Everest Sling Bag - 730 cubic inches = 11,963cm^3 = 96.9% full
Port & Company Honeycomb Sling Pack - 1,326 cubic inches = 21,729cm^3 = 53.4% full
Everest Luggage Sporty Hydration Rugged Sling Bag - 850 cubic inches = 13,929cm^3 = 83.2% full
And from what I can tell most of them are around that same size. So even in the best case the sling bag is going to be over half full and from what I can tell this are adult bags and Mami probably has a smaller child version.