On Sunday, Marco Estrada made his official spring training debut, throwing 45 pitches across two-plus innings. This after throwing 35 pitches in a simulated start the weekend before and throwing two innings in a minor league game last Tuesday. With less than two weeks of preseason games left, Estrada will only make two more starts in Florida on normal rest (roughly March 25th and 30th). It's hard to see how that leaves enough time to stretch him out even close to normal by the first week in April.
Fortunately, that shouldn't be a big deal for the Blue Jays, as their schedule is quite accommodating. After the season opening four game set in Tampa starting Sunday, April 2, the Jays have an off day which would allow them to skip the 5th spot in the rotation, and as an added bonus would let Marcus Stroman start the home opener against Boston on April 8th. In fact, with another offday the following Monday, there's no strict need for a fifth starter until April 16th. But assuming no setbacks, Estrada should definitely be ready for the second week in April, and I expect the Jays would not be looking to delay his 2016 debut unduly.
Assuming Estrada doesn't make that first start (at least), an extra spot on the opening day 25-man roster could be opened up temporarily (more on this below). The most obvious answer is to put him on the disabled list, which can be done retroactively so he would be able to start the second week in April, likely sometime in the Yankee series. A potential complication with that is that it might force him out of Spring Training games and into a minor league games, since a DL stint can only be retroactive to his last appearance. In order to be activated by April 13th or 14th, that would mean retroactive to March 29th or 30th at the latest. That's not a big deal, though perhaps less than ideal. But there's another possibility that might work even better.
Our Options and Outright Table indicates that Estrada cannot be optioned - but strictly speaking, that isn't the case. Estrada only had option years used in 2009 and 2010, leaving one option year. However, players with five years of MLB service time can block optional assignments, and have every reason to do so, which means that for all practical purposes, teams cannot option players in Estrada's situation.
But there are occasional exceptions. Last year, after making a start on July 8th, the Mariners optioned J.A. Happ to the minors on July 9th over the All-Star break until recalling him on July 20th for his next start. That allowed them to carry an extra player for seven games. Happ had the ability to block the optional assignment, but didn't since there was no downside for him: he got paid his salary regardless, wasn't intended to report to the minors, and it didn't affect his service time (players only need 172 of 183 days to accumulate a full year).
The same thing would be true of Estrada if the Jays optioned him to start the season, and would be easier than a DL stint. The only potential issue would be if Estrada was dead set on starting the year in the rotation, and consequently refused to go along with such a plan, in which case the DL would be the only option not involving his consent.
As mentioned above, this would allow the Blue Jays to carry an extra player for a first week or 10 days, not only giving them extra depth but essentially forestalling one of the decisions that will need to be made on out-of-options players. The most likely scenario in my view would be to carry an extra reliever, where there's likely to be a crunch. Drew Storen, Brett Cecil and Roberto Osuna are locks, along with a second lefty. Between Aaron Sanchez, Gavin Floyd and Jesse Chavez, at least one and probably two end up in the bullpen, leaving one or two spots in a seven man pen. Just on the 40 man roster, there are three relievers who cannot be optioned: Joe Biagini (Rule 5), Arnold Leon and Steve Delabar to say nothing of Ryan Tepera and Pat Venditte who appear to be in the running. Delabar and Leon would likely to be easier to sneak through waivers a week into the season once teams have already set their rosters.
Another possibility would be keeping an extra outfielder for the first week, with both Junior Lake and Ezequiel Carrera out of options and Darrell Ceciliani in the mix. If Edwin Encarnacion isn't ready to start the season, that could happen anyway. The final possibility would be using the extra spot to carry A.J. Jimenez, since multiple teams are apparently interested in him. If the Jays really want to keep him in the system, I think he'd be more likely to clear waivers midway through April since teams would probably be loath to claim a new backup catcher who would have to immediately learn a new staff.