It seems to me (so far) that the game is seriously crippled or even completely broken in survival modes. It's nearly impossible to make it more than 2 days now.
A major shift in tactics is certainly needed. The primary goal now seems to be to mine stone as soon as possible so we can make an oven to cook food. A single piece of raw meat effectively means death so we have to be able to cook it by the second day. Getting to stone also means we can make a stone machete.
The difficulty is compounded by having to avoid getting wet. Since it ALWAYS rains the first day, this is nearly impossible.
Here's my suggestion:
If you are in a warm biome, find the closest tree.
Cut 3 blocks of wood.
Make a table, then an axe.
Use the axe to cut as much wood as you can.
Harvest as many leaves as you can but leave a canopy to protect you from rain.
Make a wooden shovel and pickaxe, then take the table down.
Long before it gets dark, start tunnelling. (Close the entrance with leaves.)
Make campfires to light your way and tunnel to stone.
Mine stone until the pick wears out, making a space big enough to sleep with a campfire nearby.
Craft an oven, stone machete and stone spear.
Stoke your campfire completely and craft another.
(Hopefully it's warm enough that you can sleep without getting cold and catching flu.)
When you wake, make a campfire to see by and get to the surface.
Use the spear or machete to get whatever food you can.
Immediately take it to your nest and cook it.
Enjoy the good life! (Ha!)
If at any point you get flu or sick, just give up - the game is broken.
If there is no warm biome near the drop off spot, just give up - the game is broken.