Contribute to at least get the company match - you can withdraw that money as cash later if you must and pay a penalty.

For additional cash on hand, I’d try to have a budget for immediate repairs in the house if they come up in addition to an emergency fund to cover around 6 months of bills and house payments. For example what if the water heater or furnace stops working - do you have the funds to get those running again comfortably?

Also your house payment is usually a little higher than you anticipate because of utilities coming in on top of all of your estimates.