If you are a believer that Under Armour Inc. has put a challenging era behind it, then its first-quarter earnings report last week gave you some credible support for your optimism: The athletic apparel company raised its full-year guidance for earnings per share and gross margin.

One of Under Armour's most urgent priorities recently has been revamping and streamlining its supply chain, and these updated figures suggest that work is continuing apace and starting to bear fruit. Also, its inventory decreased 24% in the quarter from a year earlier to $875 million. That's a bigger dent than the "midteen" percentage-rate decline that the company had predicted for the period, and it is an important marker of progress.

And yet, caution is warranted about Under Armour's ambitious turnaround effort.

In the company's most critical market, North America, revenue fell 3% in the quarter from a year earlier. Now, that is not at all a surprise. Under Armour executives are strategically pulling back on promotions, and that can dampen sales. Also, it is planning a relaunch of its backpacks and bags in the second quarter, so the first quarter was expected to be something of lull before a big push in this category.

So, yes, the decline is explainable — but it should not be dismissed. Under Armour will only return to health when shoppers in its home market are responding more enthusiastically to its products, and when its wholesale relationships have recovered after last year's troubles. Until we see a return to sales growth in North America, I struggle to have confidence that these changes have happened. Right now, faith in the prospects of this key part of its business has to be grounded in management promises. The company bumped up full-year profit guidance, but not revenue guidance, so we don't have much reason to believe the company has seen any meaningful difference in its sales momentum.

Under Armour has a sensible-sounding medium-term strategy for returning to health. It plans to focus on product development, and the recent appointment of a new chief design officer should help bring that vision to life. Under Armour expects to tap international markets for growth and lean more on its own website and stores for sales, a model that can help with profitability and make them less dependent on unstable legacy retailers.

But the leadership team needs to demonstrate that it can pull all this off before we give it the win. Its most recent results reminded me that it hasn't done that yet.

Sarah Halzack is a Bloomberg Opinion columnist.