Buying my first property without contingencies in Milpitas

[Kenley Law]

My wife and I just moved to San Jose and we are trying to buy our first primary residence in Milpitas, to start a family. We earn a bit more than $225K combined and we only have about $120K in cash. Therefore, we are only able to put down 10%. We qualify for a loan of about $820K. We are finding it extremely difficult to buy anything, not even a townhouse. 

The market here is insanely hot and our agent is telling us that we pretty much have to put in an offer without any contingencies at all AND offer free rent back to the seller. The costs just pile up and up. 

I am most concerned about the appraisal contingency. Our agent is saying that there is pretty much no data to estimate what the appraisal will come in at, so it is completely gambling without this contingency in. I always analyze our finances in detail to value the property and calculate what we can afford to offer. Without the appraisal contingency, my affordability analysis is pretty much useless.

Is it advisable to remove the appraisal contingency? I am concerned that if I don't, I'll never be able to purchase a home, but I really can't get past the risk of opening ourselves up to a cash shortfall. I feel like I am already strapped for cash as it is. 

thank you for any advice!