This question is rife with problematic assumptions so I'll try to deal with those.

Any 'conquest' of Canaan requires a date for the Exodus out of Egypt. There are a number of dates given and argued by scholars, normally a 15th or a 13th century Exodus. So the first question is, "Which Exodus?"

As conquest intimates some sort of er, conquest of the land, this means that we should be able to find some evidence of it, and the problem is that we don't (mostly). Assuming the text is some sort of referent to reality, this means that we should be able to find evidence of the destruction of several cities, the poster-child is Jericho. This shows evidence of being around during the Middle Bronze period (circa 1700 BC), but then becomes a mildly inhabited town without any particular walls by the time(s) the Israelites come into Canaan. Assuming our modern identification of other sites are correct, the only two cities which show destruction layers are Lachish and Hatzor for the time of Joshua, which means that it's difficult to argue destruction of the places which are indicated. You might be able to argue a partial conquest (and the book of Judges indeed shows this to be true) but then that would contradict what is said in Joshua.

The other factor is that there is a whole debate about where the Israelites come from. There are a number of main theories. To hack an older comment about, here are the main theories so far, (found in Lester Grabbe's Ancient Israel 2008):

Finkelstein

produced what seems to be a true merging of Alt-Noth and Mendenhall-Gottwald, with a firm archaeological base (Finkelstein 1988). Much of his study is on the archaeology of developments during Iron I and documents the unprecedented growth of population in the hill country through this period. Although accepting that the new population included a number of elements, he especially argued that the spectacular growth came about because a large nomadic population settled down. The nomads did not come from the 'deep' desert region, however, but were the descendants of those who left settled life for a pastoral lifestyle in the Middle Bronze Age because of adverse conditions. ibid

N. Na'aman (1994c)

associates the origins of Israel with the wider developments in the eastern Mediterranean. The thirteenth to eleventh centuries brought the settlement of peripheral areas contemporary with the collapse of urban culture in the entire Aegean-Anatolian-Syro-Palestinian region and the migration of large groups on the boundaries of Mesopotamia... Traditions about patriarchal migrations to Egypt are best understood against this background; similarly, stories of coming out of Egypt such as the exodus should be understood as vaguely remembered background rather than routine migration of pastoral groups ibid

Killebrew:

These inhabitants most likely comprised different elements of Late Bronze Age society, namely, the rural Canaanite population, displaced peasants and pastoralists, and lawless 'apiru and shasu. Outside elements probably included other marginal groups, such as fugitive or 'runaway' Semitic slaves from Twentieth-Dynasty New Kingdom Egypt ... Other nonindigenous groups, such as Midianites, Kenites, and Amalekites, perhaps connected with the control of camel caravan trade routes between Arabia and Canaan, may have constituted an essential element of this 'mixed multitude.' (Killebrew 2006: 571) ibid

It's safe to say that so far, nobody agrees where the Israelites come from. One minute they are not there, then next they are (Mereneptah stele 1206 BC). It's also clear from the Biblical text that even if they did 'invade' Canaan, they didn't really conquer it, but simply took parts of it (cf Judges 1:27-35).

So there's not much evidence of the conquest as stated in the text. The way around that is to argue that the details in the Biblical text are greatly exaggerated - this was common in the ANE, but it also means that the text as a reliable referent to historical reality as we understand history is compromised.

Edit: I forgot, if you want sources for warfare in the time period (assuming a 13th century date onwards), then you could try the following, although my knowledge of the warfare during the period is not a speciality

Anthony Spalinger, War in Ancient Egypt

Donald Redford, The Wars in Syria and Palestine of Thutmose III

Eric Cline, Jerusalem Besieged from Ancient Canaan to Modern Israel

K Lawson Younger, Ancient Conquest Accounts