This is a tricky one.
Thomas Alstone and Elizabeth Podger were married 10 Jan 1670 at Chard.
This is viewable on Ancestry, and no further information is given in the entry.
(It would have useful for you to have put this in your post, rather than say ‘found documents to suggest this is correct’ - what documents?
It's always better to give any information you have found to avoid those trying to help you going over the same ground again unnecessarily).
On searching between findmypast, ancestry and familysearch, they seem to have different records. Some had baptisms, burials etc which the others didn’t.
If you go to familysearch, and search on ‘catalog’, you can find which records exist for Chard.
There are big gaps, which may well explain why you can’t find your Thomas Alstone in Chard.
The registers for baptisms run from 1649 - 1812.
Marriages 1540 - 1544, and then 1652 to 1899.
Burials from 1649 - 1812.
There is also a film for the BTs.
1603 - 1639, then 1701 - 1705.
Huge gaps.
If Thomas was married in 1670, he may well have been born between those dates of 1639 (last date of BTs), and 1649 (first date in the register).
The actual fim of the registers 1649 - 1812 is on Ancestry.
That film, and the BT one is viewable on familysearch at a familysearch library. Unfortunately not at home.
The one on Ancestry is in colour though. The ones on familysearch won’t be I should think.
There is a Jane, daughter of a Thomas Alstone baptised at Chard 1.1.1651. Possibly this was a younger sister to your Thomas.
Elizabeth Podger just makes into the registers it too - she was baptised 4.7.1650 at Chard, father Thomas Podger.
On findmypast, there are 2 indexes of a Thomas Alstone marriage to a Joan Mitchel.
One is 25 July 1639, and one 25 July 1659.
I managed to find the marriages for 1659 (eventually!) on the film on Ancestry, and Thomas Alstone is not there (there only about 3 marriages for that year).
As the 1639 index says it was from the BTs, I suspect the actual date is 1639 one, and there has been a mistranscription somewhere along the line.
Also a Robert Alstone was baptised 7 March 1629, at Chard, father Thomas.
So there are Thomas Alstones in Chard for some time prior to your Thomas married in 1670
I would be very wary of following trees posted on the internet. There have been any posts about it here on Rootschat.
I think it more likely you can’t find your Thomas because there are just no records for the years you need.
Normally I would say look for wills, as these can be a great help. I had a quick glance, and found a Thomas Podger buried in 1670. He was of Curry Rivell, which is about 15 miles away, so may or may not be the same man. It is an index only on findmypast. Didn’t spot any for Thomas Alstone though. (findmypast)
Ideas for further research:
Go through the Chard registers and glean as many Alstone names as you can.
If you are really searious, it would be a very good idea to plough through the actual film - either on ancestry or familysearch. It’s not unheard of for things to get missed, or mistranscribed, and sometimes there are other items written in the registers that never get onto just bmd transcriptions.
Do a thorough search for any wills for Alstone and Podger. Not just Thomas. Other members of the family may mention your Thomas and Elizabeth, or leave bequests to their children.
Have you searched the Somerset Archives and Local Studies catalogue for any mention of your Alstones or Podgers?
swheritage.org.uk
(i also think this is where Somerset wills will be).
Good luck!
