I had a similar situation - bought a gadget, and a few days later problems started. The main thing I figured out back then: the store might blame software glitches, but under consumer protection law you have the right to return or exchange within 14 days if the product doesn't match the stated specs. Slow performance on a new phone is exactly that kind of mismatch. The law doesn't make exceptions for software.
Before you go to the store with a complaint, do one important thing: save screenshots or video of the problem. Show how long standard apps take to load, run an internet speed test, check if the memory is full. You need this not for the store (though it'll be useful for them too), but to rule out basic stuff like background updates or a clogged cache. If after a reboot and cache clear the lag is still there - then document it.
Go to the store with your receipt and demand a written explanation of the refusal. Make sure to ask for a record of your visit and the refusal - it's an important document if it comes down to filing a complaint with Rospotrebnadzor. If the store pushes back, threaten to cite the law: consumers have the right to a quality guarantee regardless of whether it's a software or hardware fault. The phone's warranty should protect against defects, and slowdowns under normal use are a defect.