Not only do we not have physical evidence to support what happened but we have evidence AGAINST Exodus.
Considering this will be long anyway, I'm ignoring the fact that the Nile floods every year, making all Egyptian farmers unemployed who would instead be building the pyramids for their God-king. I'll ignore the insanity of having slaves build your God-kings burial chamber which was so critical to Egyptian culture, not to mention the Pharoah himself. I'll also skip the worker graves near the pyramids (hint: slaves don't get graves). I'll ignore the plagues and the politics. I'll even ignore the pursuit and whether it was the Red Sea or the Sea of Reeds. I'll simply focus on the actual journey itself.
Exodus 12:37 says 600,000 Jewish men escaped (plus wives, children, and elderly) escaped. Let's just round it down to total 500,000 people—way below estimates (which reach as high as 2 million). Let's assume that each person needs 6' of space to walk (2-3' to stand plus the next step). That creates a line of people 568 miles long (500,000 / (5280 / 6) ). Assuming they were standing next to each other, 100 people wide, that's a caravan of 5.68 miles long by at least 3' of width between people (or 300 feet wide). You can play with the numbers. This also excludes space for their belongins, livestock, and any other items. It also assumes everyone is walking, nobody is hunched over, elderly with canes, all at the same pace, etc, which further extends the line. Imagine the size of that mass of people. Also imagine that literally no other place except Exodus is this documented. No other caravans in the area saw this, no non-Egyptian government people recorded anything (assuming Egyptians whitewashed this, of which there is no evidence), no local tribes recording this, not a word from anyone.
Let's also examine the timeline. The journey took 40 years and none of the original group survived since only the non-slaves were meant to enter the new lands. 40 years is 41,600 days. On average, 12 people had to die every single day. Funerals are typically held soon after death but lets assume nobody stopped to grieve and the deceased were buried once a day, every day, for 40 years. This means we should find, on average, 41,600 grave sites of a dozen people in the area. Let's say they buried everyone for a whole week (which is severely against tradition). That only makes things worse, since they'd need to bury 84 people, which means a larger grave. But what about individual burial? Sure but, again, even if 1% of human skeletons survived, we'd still find 5,000 skeletons and I'll assume they wouldn't be buried naked, so we'd find at least clothes too. No such grave sites exist and we expect them to.
What about distance travelled? Well, a regular person can walk 3 miles/hour but let's say over time (plus belongings, etc), you drop it down to 1 mile/hour and you only walk 6 hours a day (when, in fact, people would walk faster and longer). So, 1 mile/hour, 6 hours/day - 6 miles/day. Lets bring up 41,600 day figure again and we get 249,600 miles walked in 40 years. But, hey, people are tired, need breaks, holidays, etc, etc, so let's severely round that down to a fifth of its size - 50,000 miles. That's still enough to walk the entire circumference of the Earth. Twice. What's the distance between Cairo and Jerusalem (land of Canaan)? It's 260 miles. With the 50,000 miles walked estimate, that's 200 completed trips walked in the area between Cairo and Jerusalem (considering Jerusalem and Cairo aren't on the edges of the actual territories). That's 100 full circles means they'd need to have completed more than 8 full circles per month, every year, for 40 years and all of this with the massively deflated and rounded down figures from above. If they rested in some place for a while, this would leave things behind - not only large graves (don't forget, every day, 12 dead people) but also remnants of civilization (poop, for example, not to mention broken things, torn clothes, garbage, etc).
Let's talk about food. Ranges of calories consumed during the Holocaust is between 200 and 1200 per day. Clearly the conditions during the Exodus were just as dire at best. Let's split the difference and round down—500 calories per day. So, all 500,000 people would be consuming 250,000,000 calories per day (and since 12 died every day, that's a decrease of 6,000 calories per day though, I suppose, others would be born and obviously pregnant women would need more). But let's keep to a stable 250,000,000 calorie requirement to be eaten by the entire population. Every day. A burger was created a few years ago, it was 777 pounds and had 1,375,000 calories. That's pretty good - you have meat, milk (cheese), maybe some bread - not an awful example of what food is like (assuming no sweets). From that, we need 141,272 pounds of food eaten. Every day. Let's say they only eat meat (since it's hard to grow vegetables when you travel 6 miles a day) and let's say their livestock is completely eaten and replenished once a year (which doesn't happen). That's ~51.5 million pounds of livestock they need to have with them (who, themselves, would not consume anything). A bull weighs 1600-2200 pounds. Let's say 2000 pound average for all livestock. That's 25,750 animals required and that's all eaten and replenished every single year without that livestock needing any food or drink. Let's also consider water. Women need 2.7 liters, men need 3.7 liters per day. Let's average that down to 3. That's 1.5 million liters of water they need to drink. Every day. A liter of water weighs 2.2 pounds. So, this giant caravan goes through 3.3 million pounds of water. Every day. While traveling in a desert. In case you're wondering, that's a total of 48,180,000,000 pounds of water drank in 40 years, assuming only the 500,000 people drank.
So can someone tell me how all this happened and didn't leave any evidence in the entire area? None of the logistics are plausible even with massively rounding down everything involved.
Or... it's simply a fantastic story told people who were enslaved that, yes, God will save you from your awful situation because look at all the power he has ... as long as you don't think about the details or waive them all away with miracles.