Can recent DESI BAO measurements accommodate a negative cosmological constant?

Anti--de Sitter vacuum, which corresponds to a negative cosmological constant (NCC), is theoretically important and well-motivated. However, whether it exists in reality or not has always been a highly concerning issue. In this paper, we perform the first search for NCC using recent Dark Energy Spectroscopic Instrument baryon acoustic oscillation measurements combined with Planck cosmic microwave background and Pantheon Plus supernova data. Though we did not find the evidence for NCC, we observed the indication for it. NCC is preferred at $>68%$ significance level, and we also found that such a NCC can make the evolving dark energy component (coexisting with NCC) quintessencelike, i.e., the state equation $w\ensuremath{\ge}\ensuremath{-}1$. Our work highlights the potential of upcoming cosmological surveys to search for NCC.