Whatever you do, don't mix it with your soil, or it'll leech the nitrogen out of it and cause issues. Put it on top of the soil; it'll decompose just fine on the top, without harming your soil.
Wood chip mulch is a valuable thing to have on top of your soil; plants love it. I wouldn't be worried about speeding up the process, personally.
However, if you've mixed it with the soil, that's a totally different scenario than putting it on top as mulch, and you can add extra nitrogen, or something containing nitrogen, to help it decompose faster. Don't expect plants to grow particularly well in it in during this decomposition process; expect them to be stunted and get chlorosis or else to get burned by all the extra nitrogen you add; if you have chlorotic plants in such situations--and aren't adding enough nitrogen to the soil--regular foliar sprays of nitrogen can help the plants, since the soil won't have access to that).
On top of your soil it should take about two to four years to decompose; I can't say how long it'll take if you've mixed it with the soil (but again, I don't recommend mixing it).
I'm not familiar with the specific kind of wood chip mulch (lilly pills) you have. There may be special things about it that aren't true to wood chips generally.