How do we know the asteroids formed at the same time as earth?
what evidence do we have that the asteroids indeed formed at the same time as earth?


It depends on what is your definition as "the same time". The formation of the solar system and Earth did not happen at a particular second in time but was rather a continuous process. It also depends on what you define as "asteroids".

I'll try to put some things in order.


The oldest known material from Earth is a zircon from the Jack Hills in Australia. Its age has been recently refined to be 4382 million years. We know that because we measured it.(1)
The moon forming event occurred sometime between 4348 and 4413 million years ago.(2) Now, that zircon should be younger than the moon (because the moon forming event would destroy any already-existing minerals on Earth). Yet, there is a slight overlap between the ages. This is due to the fact that analytical capabilities have their uncertainties and error.


This means that the Earth has been here at least ~4.4 billion years ago, because you need the Earth to have a moon. The Earth didn't just pop into existence, but it formed over a period of time, in which small planetesimals collided with each other and accreted to form a larger body. 

The question now is, what is the age of the planetesimals? We can't know for sure because they are all integrated into Earth, but we can look at asteroids and see their age. We do that by dating the meteorites that fall on the Earth, which in some cases are blasted off asteroids by (even more) collisions and impacts.

When you look inside a specific type of meteorites called chondrites, you can see objects that are called CAIs (calcium-aluminum inclusions). These things are solids condensed from vapourised gas that existed in the solar nebula before any planets and planetesimals formed. These are basically the first solid to form in the solar system, and they define the birth of the solar system. We know that they formed 4568(3,4) or 4569.5(5) million years ago.

Planetary bodies (which for this discussion will be considered as km-sized chucks or rock with the ability to melt and differentiate to mantle and crust, and accrete to form proper planets) began forming around 4566.2 to 4567 million years ago(5,6,7). We know that because we can date meteorites that we know originated in asteroids. This is just 2 million years after the formation of the first solid droplets in the solar system. Now, while 2 million may seem like a long time for your daily commute, it is not too long for planetary processes (considering Earth is 4.5-4.4 billion years old).

Now there is a time gap - what happened between 4566 (formation of planetesimals and asteroids) and 4413 (formation of the moon)? There are about 150 million years that I haven't talked about yet. Was the Earth gradually growing in a linear fashion during that time or did it form rather quickly? Luckily, there are answers to that as well. Based on some measured geochemical data it was shown that most of Earth's mass actually accreted ~10 million years after the formation of the solar system(8). That's rather quick! So the Earth has been sitting there, all by itself, around 100 million years until the moon formed. As to how the Earth itself formed, it could be just amalgamation of small planetisimals, collision of larger bodies, or something completely else. Chemical evidence and physical models do not always agree, and it's all highly debated.

This is a field which is rapidly evolving and discoveries are made all the time due to better analytical capabilities and better models. Just look at the years of the papers below. This is all cutting edge and a highly exciting field of study. Everything that I wrote here can be inaccurate or even plain wrong, but that's the fun in science.


  Is there any physical evidence, or is it a conclusion reached mostly through simulation?


So it is a combination of both. You find physical evidence: rocks from Earth and parts of meteorites and their minerals. You measure their isotopic composition to find their age and other characteristics. Then you make a model (or a simulation) that tries to see what has to happen in order for the physical properties to agree.

Further reading:

An introduction to Meteorites and the origin of the Solar System - a very accessible and interesting read.

Chronometry of Meteorites and the Formation of the Earth and Moon - a more technical review, may be paywalled.


Refs:


1 Valley, J. W., Cavosie, A. J., Ushikubo, T., Reinhard, D. A., Lawrence, D. F., Larson, D. J., … Spicuzza, M. J. (2014). Hadean age for a post-magma-ocean zircon confirmed by atom-probe tomography. Nature Geoscience, 7(3), 219–223. doi:10.1038/ngeo2075



2 Carlson, R. W., Borg, L. E., Gaffney, A. M., &amp; Boyet, M. (2014). Rb-Sr, Sm-Nd and Lu-Hf isotope systematics of the lunar Mg-suite: the age of the lunar crust and its relation to the time of Moon formation. Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, 372(2024), 20130246. doi:10.1098/rsta.2013.0246



3 Bouvier, A., &amp; Wadhwa, M. (2010). The age of the Solar System redefined by the oldest Pb–Pb age of a meteoritic inclusion. Nature Geoscience, 3(9), 637–641. doi:10.1038/ngeo941



4 Burkhardt, C., Kleine, T., Bourdon, B., Palme, H., Zipfel, J., Friedrich, J. M., &amp; Ebel, D. S. (2008). Hf–W mineral isochron for Ca,Al-rich inclusions: Age of the solar system and the timing of core formation in planetesimals. Geochimica et Cosmochimica Acta, 72(24), 6177–6197. doi:10.1016/j.gca.2008.10.023



5 Baker, J., Bizzarro, M., Wittig, N., Connelly, J., &amp; Haack, H. (2005). Early planetesimal melting from an age of 4.5662 Gyr for differentiated meteorites. Nature, 436(7054), 1127–31. doi:10.1038/nature038825


6 Greenwood, R. C., Franchi, I. A., Jambon, A., &amp; Buchanan, P. C. (2005). Widespread magma oceans on asteroidal bodies in the early Solar System. Nature, 435(7044), 916–8. doi:10.1038/nature03612



7 Amelin, Y., Kaltenbach, A., Iizuka, T., Stirling, C. H., Ireland, T. R., Petaev, M., &amp; Jacobsen, S. B. (2010). U–Pb chronology of the Solar System’s oldest solids with variable 238U/235U. Earth and Planetary Science Letters, 300(3-4), 343–350. doi:10.1016/j.epsl.2010.10.015



8 Rudge, J. F., Kleine, T., &amp; Bourdon, B. (2010). Broad bounds on Earth’s accretion and core formation constrained by geochemical models. Nature Geoscience, 3(6), 439–443. doi:10.1038/ngeo872