Help! Ticking noise coming from C250 on startup

Looking for some advice since I'm struggling to get an actual diagnosis. I have a 2014 C250 Mercedes that's in very nice shape but does have a lot of miles (126k). Awhile back I noticed a ticking noise when starting it. It only lasts a couple of seconds on a cold start and goes away. There are no other symptoms. I took it to a non-mercedes mechanic who said they thought it was the timing chain and that it's not something they themselves would repair. So I took my car to my local Mercedes dealership for a second opinion. I told them it had been diagnosed as a timing chain issue and I wanted confirmation and a quote. Their diagnostic fee was $220 but they called me and told me that in order to really diagnose the car, they had to remove the valve covers (if I remember correctly) and it would cost me an additional $1400 to confirm. So I asked if I had to have a timing chain replaced how much it would be and they told me likely around $10k so I told them to wrap it up. Anyone think it's worth getting the oil changed (because it is due for one) to see if it could be the hydraulic valve lifters and not the timing chain? I don't want to keep putting money into the car if it's really a timing chain because the car is not worth anything at this point. Only symptom, slight tick for a couple of seconds on cold start. Doesn't happen while driving and I'm not experiencing a performance issue. Any input would be appreciated! Thanks!