I can have the core burner building part of it up and running by around minute 7 or 8.
I like to prebuild most of it before automation is fully researched, so I have it as soon as the last science pack is consumed. GC and gears for assemblers are already hand crafted, and I'm removing the boxes for collecting stone as that last pack is researched.
Note that automation research takes 10s to use up a science pack and you can hand craft one in 5s. So, building your ore production in parallel to crafting the science packs is probably the most optimal. I've practiced queueing up the entire sequence of red science/burner/inserter/red/burner/inserter/furnace, etc in one go. I'm sure having lots of large queue sequences memorized or written down is useful, but that's the only one I've done so far. Alternatively, you can aim for 2 labs, in which case that's not true, but I haven't seen a case yet for doing 2 labs to start.
The nice thing about the blueprint below is that it builds burner/furnace pairs as you go along, allowing you to incrementally build production, which is more optimal than doing it all at once. See the complete thread here - viewtopic.php?f=5&t=92934
I hand pull from the iron furnaces if it's building too fast.
You can also temp switch it over to belts or inserters if you need some of those. For inserters, you'll need to hand feed some GC tho. This can be useful for green research which takes belts/inserters.
You can also use burner inserters without the gc hand feed, but burner inserters can be a bit finnicky to hand feed. Z dropping quickly tends to miss some (maybe I don't have the right technique yet, tho). They also suck up coal rather fast if they are very active. They aren't that bad for furnaces tho where they require infrequent refueling. Also, coal is rather precious at the beginning when they'd be most useful. 1 coal can produce about 5 or 6 ore, and burners take 3 ore versus 5.5 regular inserters.
That all said, I'm going to experiment a bit more with them. Burner inserters have a fond place place in my factorio heart. They don't require power poles and they might be cheap enough to spam.
I find the extra furnace assembler useful, though might not need that right away. Iron ore prod is likely better early on.
It does, of course, require stone to border an iron ore patch. maps with iron/stone/copper/coal all meeting close by are good at the beginning.