Probably. Call the other attorney. See if they will reset it. If not, show up in court and ask that it be reset. Be prepared to tell the court what steps you have taken to find an attorney.
You can ask to have it reset, as it is not your hearing - do call opposing counsel directly to if they are agreeable to the reset (you might have to agree to some terms in the interim when y'all can negotiate further or have the judge rule on a temporary basis. I would also suggest sending a request for an extension in writing, and save proof of your request(s) to take to court if you don't receive a response. You should be prepared to appear in court the day you've been noticed (even though it is well before your answer date) and ask the court for a reset of a few weeks so that you can hire counsel and perhaps even attend mediation. You might also call the court and speak with the clerk to see if you need to be prepared with anything else (just remember to have your cause number ready when you make that call, and don't call before 11am - the mornings are always busiest).
"Most" of the time if a person says they were just served with papers and need time to hire an attorney, the court will work with them. In all likelihood you will be sworn to return to court on a day and time certain so that the other side does not have to get you served again. And it's likely the other side will want some orders in place while you look for a lawyer. The usual amount of time for you to find a lawyer was a couple of weeks, but in some courts it could be as long as 6 weeks. Custody matters are important, not just to the parents but also to the child.
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