Watching a client go through this exact situation right now, and it's déjà vu. Back when I ran customer success for a small agency, one of our accounts hired an outside SEO consultant and expected leads by week three. Every check-in call turned into the same argument because nobody had framed what "progress" actually looks like up front. Learned a lot watching that relationship fall apart.
Here's how I look at it now. Real progress typically shows up inside of three to six months, and the definition of progress matters a lot. The gold standard is organic leads that convert to revenue, because organic revenue is the actual goal. Fair warning: that one's hard to pull off and depends on solid revenue operations behind it.
Fallback goals, in roughly descending order of usefulness: more organic leads, more organic traffic, and before anyone even hits the site, growth in impressions, visibility, or the number of keywords you're ranking for.
The honest truth is that clean outcome-based goals are tough to write for SEO. It's not the right channel for every business, either. Whether it works for a specific company depends on the market, the audience, and especially the customer journey. A huge chunk of SEO success is downstream of other work like dev, design, copy, conversion rate, social, PR. A genuinely good consultant will advise across those buckets and can tell you "traffic growth in a quarter, IF x, y, and z happen in the other areas."
That said, input goals aren't a cop-out. For some businesses, paying for a set number of page optimization plans, new content, schema builds, or similar deliverables makes total sense, since a healthy program needs all of that anyway. Search is a monthly and yearly game, not a daily or weekly one. Serious organic lead flow takes most companies years to build, especially in crowded, established markets. Input goals let a business invest gradually and stack up the authority needed to eventually win in search.
Hope that helps the OP.