PA-28 pilot reported entering IMC from VFR at the filed destination. The pilot did not hold an instrument rating and completed an IFR approach with help from ATC.

Narrative

I departed in my own aircraft; Aircraft X; from ZZZ1 at approximately headed directly to ZZZ. I flew to meet with my family for a event. My only passenger was my younger brother who has flown with me prior to this event. My aircraft is IFR certified and is the same aircraft I completed my instrument training in. However; I have not yet completed my instrument checkride scheduled for ~two weeks from today. To date; I have logged 40+ hours of simulated or actual instrument conditions with a CFII. Prior to takeoff from ZZZ1 all METARs; TAFs; and other meteorological data derived from my EFB had forecasted ceilings above 4000 ft. with visibility over 10 miles - well above published VFR standards and my own personal minimums with a runway elevation of ~500 ft. at ZZZ. My initial VFR flight following request with ZZZ1 was for 4500 ft. Shortly after takeoff; I learned en route that I would have to descend below my requested altitude based on data on my EFB. I communicated my intentions with Center to descend to 3500 ft. to maintain VFR throughout the state border - which I did and did successfully maintain VFR. I maintained VFR until approximately 6 miles from the ZZZ.The Controller I was speaking with on Approach was extremely helpful and communicative. I first spoke with him at least 20-30 miles from ZZZ. On my initial call; I checked in with him reporting my altitude and asking for known conditions surrounding ZZZ. The Controller proceeded to ask multiple aircraft the altitude in which they broke out of clouds. He proceeded to communicate with me the pilot reported ceilings. Every pilot responded that the ceilings were around 3000-4000 ft. Knowing this information; he proceeded to ask me if my aircraft was IFR equipped; to which I responded yes. He followed asking me if I was personally IFR rated; to which I responded 'No; but I am checkride ready.' After the fact; he proceeded to ask me if I wanted to continue with vectors for the ILS XX at ZZZ and to switch to the Tower frequency. I responded with a resounding 'Yes; I already have the ILS frequencies plugged in as well as the RNAV XX. Aircraft X will continue with vectors for ILS XX.'At this point in time; I was below the clouds at ~2700 ft. and there was a slight mist of rain in the air. The ceiling that I observed at this moment were ~3000 ft. MSL. I then asked Approach what the MDAs were for my area; in which he proceeded to report to me 2500 ft. with some 2700 ft. and 3000 ft. areas to the northwest of ZZZ. Next; Approach vectored me to intercept the localizer (which was already plugged in on both of my comms). After his instruction and confirmation; I then switched to the Tower frequency after thanking the Controller for his help.After switching to the Tower frequency ~6 miles from ZZZ; I reported to him 'Tower; Aircraft X inbound ILS XX quickly losing visibility.' He responded; asking me if I wanted to proceed. I responded; 'Yes; I am prepared for the situation.' It was at this moment that I inadvertently flew into IMC shortly before approaching ZZZZZ (the published FAF) on the ILS XX at the published altitude of 2500 ft. I reported my situation to the Tower and he communicated to me my missed approach instructions of 'runway heading; 3000 ft.'. By this time I had intercepted the localizer; but had trouble staying on course horizontally mostly due to turbulence and winds. It is important to note that my glide slope indicator was very much on point throughout the approach. At this point; I also gave my sole passenger (my brother) instructions to keep an eye on my vertical speed indicator (and to report to me if my descent is greater than 1000 fpm) and to search for the runway lights. Prior to this moment; the Tower told me that they had increased their runway lighting to maximum brightness. Shortly after; I was on course at ZZZZZ1 ~4 miles from the runway touchdown point. I crossed ZZZZZ1 at the published 1560 ft. The published minimums were 701 ft. At ~850 ft. my brother and I both clearly saw the runway lights; I was near perfectly on course with the ILS; and we proceeded to successfully and safely land. The Tower had congratulated me and warmly welcomed me to ZZZ. I responded; 'Sir it feels great to be on the ground and to be here. Thank you for all your help.' I proceeded with progressive taxi instructions to the FBO. I had landed at ZZZ in clear conditions twice before in the proceeding 3 months. It is important to note that I had been tracking this weather for 2 days prior to my departure from ZZZ1. The night prior; I had received a bit more than 7 hours of sleep; with 7 hours being my normal. At the moment of departure; the weather forecast was very different from what was experienced. I am thankful to have successfully overcome the situation with a high level of skill for a technically non-IFR rated pilot; nonetheless a pilot which exceeded the published standards for taking a IFR check ride. My check ride had not been completed at this moment simply due to the time of the year - a very busy season for myself and most. Thankfully the outcome of this situation was successful and I learned much from it as I logged my time after touchdown. I never would have flown to ZZZ with knowledge of the unexpected conditions present.