Absolutely. Check out side channel attacks. The problem here isn't about software exploits, but hardware issues. https://en.wikipedia.org/wiki/Side-channel_attack
Some things to get you started: Meltdown and Spectre: https://en.wikipedia.org/wiki/Meltdown_(security_vulnerability), https://en.wikipedia.org/wiki/Spectre_(security_vulnerability)
Rowhammer: https://en.wikipedia.org/wiki/Row_hammer
These are exploited by malicious processes doing something to the hardware which may result in information about your process(es) being leaked. Now, if this is on your computer, then the chances of encountering a malicious process that exploits this hardware bug would be low.
However, when you move this scenario to the cloud, things become more possible. Your vm/container is being scheduled on CPUs that may/may not be shared by other containers. All it would take is for a malicious guest VM to be scheduled on the same core/CPU as you and try exploiting the same hardware you're sharing.