Cross-scale coupling from magnetohydrodynamics (MHD) to non-MHD scales is important in interpreting observations of explosive events in nature, such as solar flares and geomagnetic storms1,2. Experiments and observations also link it to the emergence of energetic particles and X-rays3. However, how this multi-scale physics affects the abrupt onset of reconnection remains unknown. Here we report observations from laboratory experiments involving two flux ropes with electron beams that induce magnetic turbulence and then abruptly merge into a single structure, altering the magnetic topology in the MHD regime. Two separate electron beams are launched along magnetic field lines and form individual flux ropes with a drift velocity higher than the ambient Alfvén velocity, effectively driving magnetic turbulence through beam-driven instabilities, as inferred from the increased level of the turbulent power spectrum. Experimental observations, including the appearance of energetic particles, increased ion temperature and changes in the characteristics of the flux ropes, suggest that beam-driven turbulence drives three-dimensional (3D) reconnection. 3D particle-in-cell simulations are performed, which successfully reproduce the key aspects of the experiment. These results directly explain how non-MHD kinetic processes progress through multiple scales to induce global MHD changes.