Perhaps take a look at the Pier Engineering thread here on Cloudy Nights. Your construction will be much simpler if you can (and feel comfortable with) using an auger to drill a deep shaft as the footer for your steel piers, rather than having a big block of concrete at a shallower depth. If you accept the "deep shaft" footer, you can:
Set your forms for your floor, and even place and tie your rebar, just don't raise the rebar onto chairs yet as you'll be walking on it. Then drill your pier footer shafts with your auger and remove all the "spoils". Set the rebar cage, the forms for the very tops of your pier footers, and the anchor bolt template with your anchor bolts. Note that the forms for the top of your pier footers will be "double": one inner form to create the shape of the top of your pier footers (and to support your anchor bolt templates), and an outer form to keep the floor concrete from getting into contact with the top of your pier footers.
You could also ask your concrete contractor to pour your floor, leaving a couple of holes and come back in a couple of weeks with your auger and drill for your pier footers. Once you get the forms for the tops of the piers and your anchor bolts set you could pour the concrete for your piers yourself.
When your concrete contractor arrives, he'll pour your pier footers first, making sure your anchor bolts are oriented correctly and are plumb. Then he'll raise the rebar for your floor onto chairs (or pieces of concrete bricks) so the rebar is held near the middle of your floor slab. Next he'll pour the floor and rake the concrete such that it fills the forms and is approximately level and smooth-ish. Then he'll screed the top surface: he'll drag a straight edge, supported by your forms, over the wet concrete to remove excess and bring your floor to the right elevation. I'm sure your anchor bolts will get in his way, but he'll deal with that. Finally, after a few hours, when the concrete has just begun to set, he'll "float" the concrete with a big metal plate to flatten the concrete and make it smooth. If you plan to leave the concrete exposed, he may recommend a "light broom finish" to slightly roughen the concrete so it's not slippery if it gets wet (like with dew when your roof is open).
If you decide you want a big chunk of concrete, you'll have to dig a big hole and pour that part first. Then you'll back-fill over the top of the footer and make sure your back-fill is well and properly compacted so it doesn't settle and create a void under your floor. Then you can build your forms, set your rebar and pour your floor.
An alternate to the plan above is to make the top of the "big chunk footer" the same elevation as the finished concrete floor. Then it would be possible to execute construction is a manner similar to the deep shaft footer.
Good luck with your project.