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We present a comprehensive study of both continuous-wave and first mode-locked operation of a diode-pumped Yb:Ca3La2(BO3)4 laser in the soliton regime. Using a 976-nm single-spatial-mode, fiber-coupled InGaAs diode laser as pump source, the Yb:Ca3La2(BO3)4 laser delivers a maximum continuous-wave output power of 491 mW at 1050.6 nm, with a slope efficiency of 63%. Passive mode-locking is realized using a commercial semiconductor saturable absorber mirror, generating soliton pulses as short as 35 fs at 1055.9 nm, with an average output power of 96 mW at a pulse repetition rate of ∼66.5 MHz. By optimizing the output coupling, the average output is scaled to 239 mW for slightly longer 48-fs pulses at 1051.9 nm, corresponding to a peak power of 65.9 kW and a laser efficiency of 29%. These results highlight the potential of Yb:Ca3La2(BO3)4 as a gain medium for sub-50-fs ultrafast laser applications.