  We study transient effects in a setup, where the quantum dot (QD) is abruptly
sandwiched between the metallic and superconducting leads. Focusing on the
proximity-induced electron pairing, manifested by the in-gap bound states, we
determine characteristic time-scale needed for these quasiparticles to develop.
In particular, we derive analytic expressions for (i) charge occupancy of the
QD, (ii) amplitude of the induced electron pairing, and (iii) the transient
currents under equilibrium and nonequilibrium conditions. We also investigate
the correlation effects within the Hartree-Fock-Bogolubov approximation,
revealing a competition between the Coulomb interactions and electron pairing.
