So is it
literally 1 minute for the game to startup? If so there might be a bigger issue than the hardware side. Time the startup time for me, let me know how many seconds it takes to start up.
Your cpu is pretty weak, not the worst out there but certainly not very current. I can't find your RAM or HDD listed here. I'm willing to bet though, it's a 5400 RPM HDD with no SSD and 4GB of RAM. If you have more accurate details let me know. You can find your HDD details by doing the following:
1. Press Windows+R on your keyboard
2. Type devmgmt.msc then press enter
3. Look on that list for something called disk drive, click the triangle next to it to expand the list. Let me know the names of everything listed here.
I should be able to find the Hard drive speed based on that.
Start up times for games is going to factored by 3 components on the hardware side. Your CPU which we've concluded is fairly weak, your RAM size and it's speed. Finally the hard drive and it's read/write times. With a lower powered computer I would expect the startup times to be on the longer side, but like I said before, if it is
literally a minute then there is a possibility of an issue we can fix.
Something you have to remember though is launching and running that game is not the only thing your computer is doing at the time, it also has to handle everything in the background. You say this has been doing it since day 1 which leads me to believe it's a hardware issue, although, if you can clean up what your computer is doing in the background we may be able to shave off some loading time. Lets start by getting a feel for everything running.
1. Press ctrl+shift+esc to open task manager
2. We need a detailed view so in the bottom left corner press "detailed view"
3. Give me a screenshot of all the process running listed here (you may have to make the window taller and get multiple screenshots so I can see everything listed)
In addition lets talk about some fixes some folks have done to decrease the startup time.
1. Reinstall Terraria.
2. Launch Terraria, press ctrl+shift+esc which will open task manager, find the Terraria application right click it and then click "set priority", then select "high"
3. Verify the integrity of your game cache through steam.
4. Run a virus scan. There are many free services that will allow you to do this, my preference is avast.
5.
Download and install Ccleaner run the program and click "analyze" at the bottom, then click "run cleaner". After it deletes all the junk files it finds click the "Registry" tab on the left side of the program. Now click "Scan for Issues" then click "Fix Selected Issues"
If none of that helps it's most likely a hardware issue and not a software issue that we fix reliably. If you have any questions on how to preform any of the tasks above let me know and I'll go into a more detailed explanation on how to do it.