For a brand-new domain, expect the easiest long-tail local terms - specific neighborhood or service combinations with low competition - to start showing measurable movement around six to ten weeks after launch, assuming the site is technically sound and the Google Business Profile is fully built out.
More competitive city-wide terms ("kitchen remodeler [City]" without a neighborhood modifier) typically take three to six months to show meaningful ranking, and the most competitive head terms in dense metros can take six to twelve months or longer, since they're competing against established sites with years of accumulated authority.
The honest takeaway: organic search should never be your only lead source in the first few months of a new site. It's the channel that compounds and eventually costs close to nothing per lead - but it needs outbound, referrals, or paid ads to carry you while it ramps.