Yes. You will need furnace technology of, surprise, iron-age level (2500BCE, for example). A fairly pure iron-oxide dust is equivalent to an extremely high-grade iron ore. The oxides are reduced by carbon monoxide produced by burning high-carbon fuel (eg. charcoal) in a hot, low oxygen environment (eg. a blast furnace). See https://en.wikipedia.org/wiki/Bloomery
The iron compound in haematite is an iron oxide ($Fe_2O_3$) and an important iron ore... magnetite is another ($Fe_3O_4$). Any ore that contains a large percentage of either can be fed directly into a blast furnace to produce iron, and there are relatively straightfoward ways to process lower grade ores to make them useable in the same way.
Rust is commonly a mixture of hydrated iron oxides and hydroxides, and those same chemicals are found in a less concentrated form in limonite which is yet another common iron ore. You can also find stuff like bog iron from relatively shallow surface excavations. It was the major source of iron used by vikings. A major constituent is an iron oxyhydroxide, $FeO(OH)$, also found in goethite... yet another commercial iron ore.
The pigment in ochre is an iron-bearing compound like haematite, limonite or goethite, so I'm pretty certain that could be used too. The take home message should be that rust, "iron oxides" and iron ores are all more or less indistinguishable other than the kind and quantity of impurities in them.
One last comment, though.
Could an early people with relatively little access to iron mines use... the red dust on Mars to smelt/forge iron objects...
This specific case would prove tricky, as you need a supply of carbon rich fuel for the reduction processes humans use and have used. On earth, we use living trees (processed to make charcoal) or dead ones (which formed coal, then processed to make coke) and Mars has neither a biosphere nor (probably) any fossil fuels. It also didn't have any "early people", of course.
It may be that other metals are more useful on Mars if they can be refined without carbon. Aluminium and magnesium are possibilities there. There are probably also other ways to reduce iron oxide without carbon, but I'm not familiar with them.