You would need a new cable. Plugging an unbalanced headphone into a balanced output via adapter can damage your equipment. You can do it the other way around; you can plug balanced headphones into an unbalanced output using an adapter without issue. But unbalanced headphone into balanced output = broken stuff.
Reason being, a headphone has two drivers, each driver has two poles, a positive and a negative. So you're dealing with Left+, Left-, Right+, Right-. In a traditional unbalanced connection, the two negatives are shorted together, reducing the connector to three poles, L+, R+, and Ground. In balanced, the two negatives are kept separate, so it remains L+. L-, R+, R- at the connector. This is why you can adapt a balanced headphone to an unbalanced output, all you need is an adapter that receives the four poles and shorts the two grounds that hadn't yet been shorted, and outputs L+, R+, Ground at the other end. But you can't adapt an unbalanced headphone to a balanced output, because once the two negative poles are combined, they can't be separated back out. It's like if you had red water and blue water, combined them, and then tried to separate them back out again. Can't be done. You're just stuck with purple water and there's no going back. Similar thing here, once you unbalance the headphones by combining the two negative poles, there's no way to separate them again to re-balance them, and trying to do so will just risk damage to your amp, or headphones, or both.
In regards to making the Sivga balanced, luckily the headphone's design makes it easy, with the cable detachable at each individual earcup. I don't own this headphone, so hopefully an actual owner can verify this for me, but according to the Amazon page, the connectors at the earcups are 2.5mm. So you would need a cable that's dual 2.5mm at one end and 4.4mm balanced at the other end, which is something like this:
https://smile.amazon.com/Youkamoo-Compatible-Version-Headphones-Replacement/dp/B096LXF8GH
There's a chance Amazon's Sivga page is wrong and it's actually dual 3.5mm connectors at the cups, so I'm hoping an owner here can verify that for me. But either way, dual 2.5mm or dual 3.5mm to 4.4mm balanced cables are pretty common (Hifiman headphones used to use dual 2.5mm and currently use dual 3.5mm), and by virtue of being common and non-proprietary they can be had pretty inexpensively.