(1) Background: Human milk oligosaccharides (HMOs) may support immune protection, partly via their action on the early-life gut microbiota. Exploratory findings of a randomized placebo-controlled trial associated 2′fucosyllactose (2′FL) and lacto-N-neotetraose (LNnT) formula feeding with reduced risk for reported bronchitis and lower respiratory tract illnesses (LRTI), as well as changes in gut microbiota composition. We sought to identify putative gut microbial mechanisms linked with these clinical observations. (2) Methods: We used stool microbiota composition, metabolites including organic acids and gut health markers in several machine-learning-based classification tools related prospectively to experiencing reported bronchitis or LRTI, as compared to no reported respiratory illness. We performed preclinical epithelial barrier function modelling to add mechanistic insight to these clinical observations. (3) Results: Among the main features discriminant for infants who did not experience any reported bronchitis (n = 80/106) or LRTI (n = 70/103) were the 2-HMO formula containing 2′FL and LNnT, higher acetate, fucosylated glycans and Bifidobacterium, as well as lower succinate, butyrate, propionate and 5-aminovalerate, along with Carnobacteriaceae members and Escherichia. Acetate correlated with several Bifidobacterium species. By univariate analysis, infants experiencing no bronchitis or LRTI, compared with those who did, showed higher acetate (p < 0.007) and B. longum subsp. infantis (p ≤ 0.03). In vitro experiments demonstrate that 2′FL, LNnT and lacto-N-tetraose (LNT) stimulated B. longum subsp. infantis (ATCC15697) metabolic activity. Metabolites in spent culture media, primarily due to acetate, supported epithelial barrier protection. (4) Conclusions: An early-life gut ecology characterized by Bifidobacterium-species-driven metabolic changes partly explains the observed clinical outcomes of reduced risk for bronchitis and LRTI in infants fed a formula with HMOs. (Trial registry number NCT01715246.)