So far as changing the topology of spacetime, NASA is (or was) investigating it as part of Alcubierre/Warp drive research[1]. That being said, a warp bubble is a far simpler goal than a wormhole.

> According to White, these results showed a vanishing but non-zero difference between charged and uncharged states after signal processing, but this difference remains inconclusive due to external interference and limits in the computational processing.

[1]: https://en.wikipedia.org/wiki/White%E2%80%93Juday_warp-field...