Straight Talk - Head Gasket

Put a vertical strip of masking tape on the reservoir, mark the level with a sharpie.

 

It is kind of amusing when the op states many times no diy is possible but people keep suggesting it. However diagnostic methods on a gen3 Prius can be different and a smart owner may want to understand the options before paying a shop. I would certainly go to a recommended hybrid shop when possible.

An early head gasket "rattling" symptom is very loud, sounds like metal to metal contact, causes the car to shake violently and initially convinces people the engine is blown.

Until it smooths out seconds later and drives great for the rest of the day and sometimes for days to weeks without repeating. If it is a head gasket severe rattling will occur at some point.

There are egr based shudders and stalls possible but those are caused by a sticking open egr valve, not a clogged egr system. No metal to metal rattling. A Toyota Techstream scanner can run an egr step test while monitoring intake manifold pressure.

An egr flow blocking test can be done by any shop without a Techstream scanner. Video below.

Some owners want to do something. Maybe "preventative" or "parts cannon" spark plugs, egr system cleaning, ignition coils or fuel injectors when the first few items are indecisive. Those owners typically throw away $1,000 to $2,000 in this kind of blind part changing. Resist the temptation when the car runs smooth after the rough start. If the problem continues when running most shops have techniques to isolate a bad plug, coil or injector.

Based on your description you are not there yet.

A borescope inspection of the cylinders performed by someone who has seen a hg problem on one of these engines is the best diagnostic for a gen3 head gasket problem BEFORE it is bad enough to lose coolant or fail a combustion gas in coolant test.

Again you are unlikely to be there yet.

Egr block flow test

At about 10:15 in the video he starts talking about the egr valve letting "air" into the intake manifold. He means exhaust gasses.

Car Care Nut HG Borescope at 660s

Finally, gen3s and high mile reliability issues are real and exceed most other Toyota's in frequency and cost. Brake Boosters, Inverters and Hybrid Batteries are other expensive concerns and those things along with head gaskets are what Tom was talking about. Sometimes it is hard to be comforting when you are talking about a vehicle needed as a lifeline.

 

It doesn't hurt to understand the process, even if you don't execute it personally.

 

you can call toyota customer service and try pleading your case nicely. sometimes they help and sometimes not.
but first, you will need a misfire trouble code and dealer diagnosis

 

A Prius owner who has had all of two, non-clattery, rough cold starts, in isolation, followed two days later by a cold start that wasn't rough at all, isn't a person who needs a misfire trouble code or a dealer diagnosis or any of this conversation, but seriously needs a relaxing funny movie and some chocolate.