Does Stellar maintain a set of nodes to achieve quorum intersection? If not, how can a Stellar network achieve quorum intersection at all times, meaning no disjoint quorums at all in the network?
Yes. Stellar Development Foundation (SDF) maintains three validators, which you can find in this list of validators. If you include at least one of them in every quorum slice, you will stay in sync with SDF and hence very likely with the rest of the world.
Down the line, however, other entities may come to be perceived as more important than SDF (e.g., maybe IBM), in which case you should add those entities as well. The configuration format is hierarchical, so you can require, for instance, one SDF node and one IBM node in every quorum slice. If there is an exchange or token that you rely on, then you should also include the exchange or token issuer if they have validators.