Magnetic Weyl semimetals (WSMs) have been presumed to be immune to proximity-induced spin-singlet superconducting pairing due to a chirality blockade of the regular Andreev reflection. In this work, we study all possible superconducting pairing induced in a WSM sandwiched between two conventional superconductors in a Josephson junction setup. We confirm that, while conventional intraorbital pairing is present on the surface of the WSM, it cannot propagate into the bulk due to the chirality blockade. However, interorbital pairing, with both even-frequency spin-singlet and odd-frequency mixed-spin-triplet symmetry, propagates into the bulk of the WSM, as do several symmetries. To demonstrate the importance of these finite interorbital and pair amplitudes in an experimental setup, we calculate the Josephson current and find a finite and even increasing current when the chirality blockade effect for the conventional intraorbital pairing is enhanced.