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The recently discovered system Gaia 0007−1605 consisting of a white dwarf (WD) with a close brown dwarf companion and a distant WD tertiary very much resembles the triple system containing the first transiting planet candidate around a WD ever discovered: WD 1856+534. We have previously argued that the inner binary in WD 1856+534 most likely formed through common envelope evolution but triple star dynamics represent an alternative scenario. Here, we analyse different formation scenarios for Gaia 0007−1605. We reconstructed the potential common envelope evolution of the system and found that assuming standard parameters for the energy budget provides a reasonable solution. In agreement with other close white dwarf + brown dwarf binaries, and in contrast to WD 1856+534, no energy sources other than orbital energy during common envelope evolution are required to understand the current configuration of the system. In addition, using analytical prescriptions for triple dynamics, we show that Von Zeipel–Lidov–Kozai oscillations might have triggered tidal migration due to high-eccentricity incursions (e ≳ 0.997). We conclude that the inner binary in Gaia 0007−1605, as its sibling WD 1856+534, formed either through common envelope evolution, triple dynamics, or a combination of both mechanisms. [ABSTRACT FROM AUTHOR]