Hi tsengf,
A box spring has springs inside it that flex under the mattress and there are very few one sided mattresses today that use them as a support system and in many cases they will invalidate a mattress warranty. Most mattresses today need a steel or wooden bedframe with a foundation that has minimal to no flex (vs a box spring that flexes) or a platform bed which also has little to no flex under the mattress. There are many in the industry that mix up the terminology between box springs and foundations even though they are very different products.
A foam mattress like Tuft & Needle will generally do best with a firm, flat, and evenly supportive support surface underneath it that has minimal to no flex under the mattress and for larger sizes with at least one center support beam that has good support to the floor to prevent any sagging in the middle of the mattress. The components need to be strong and durable enough to support the weight of the mattress and the people sleeping on it without some of the parts bending, sagging, or breaking over time. The support surface under the mattress should have enough surface area to prevent the foam in the mattress from sagging through any gaps or spaces in the support surface over time but still allow some airflow under the mattress.
There is more information about the different types of support systems that are generally most suitable for different types of mattresses in post #1 here with a few examples of each of them and there are also some comments and information in this topic that would apply to any foam mattress as well.
Their website here says it’s 10" thick.
Phoenix